Overview

Randomized vaccine trials are used to assess vaccine efficacy and to characterize the durability of vaccine induced protection. There is a broad consensus that placebo volunteers in COVID-19 vaccine trials should be offered a vaccine once efficacy has been established. This will likely lead to most placebo volunteers crossing over to the vaccine arm, thus complicating the assessment of long term durability.

In this vignette, we provide code for simulating COVID-19 vaccine trials and assessing vaccine efficacy (VE) and durability of vaccine induced protection within a Cox proportional hazards framework. The code supplied in this vignette reproduces the example trials in Fintzi and Follmann (2021), but is flexible and can be modified to accommodate staggered entry, frailties, waning or constant VE, and various study designs including placebo-crossover, continuous crossover, or standard parallel arm trials.

Setup

We will simulate a COVID-19 vaccine trial where the true VE waned linearly on the log–hazard scale from 85% to 35% over 1.5 years. The trial enrolls 30,000 participants with linear accrual over three months in a 1:1 randomization to vaccine or placebo. The baseline attack rate is piece–wise constant, with change–points every three months, and is calibrated to yield 50, 75, 50, and 25 cases on the placebo arm in each period in the first year, and half the expected number of cases per period on the placebo arm in year two. In this example, interim analyses are planned at 150 cases, which ultimately result in crossover at the end of year one following evaluation and vetting of the efficacy by a regulatory agency. Placebo crossover occurs over a four week period. Each volunteer is followed for a total of two years.

Let \(t\geq 0\) index time since study initiation, and let \(\boldsymbol{\tau}= \left\lbrace\boldsymbol{\tau}_i = \left(\tau_i^{(e)},\tau_i^{(v)}\right); \tau_i^{(v)}\geq\tau_i^{(e)}>0,\ i=1,\dots,N\right\rbrace\) denote the times of study entry and vaccination for the study participants. Define \(Z_i(t)\) to be an indicator for whether \(t>\tau_i^{(v)}\). We will suppose that vaccine efficacy decays linearly on the log-hazard scale. The hazard for participant \(i\) is, \[\begin{align} \label{eqn:loglin_decay_haz} h_i(t) &= \left\lbrace \begin{array}{ll} 0 &,\ t\leq\tau_i^{(e)}, \\ h_0(t)\exp\left[Z_i(t)\left(\theta_1 + \theta_2\left(t-\tau_i^{(v)}\right)\right) \right] &,\ t > \tau_i^{(e)}. \end{array} \right . \end{align}\] Here, \(VE(t) = 1 - \exp\left[\theta_1 + \theta_2\left(t - \tau^{(v)}\right)\right]\). The baseline hazards, \(h_0(t) = \gamma_\ell,\ t \in (t_{\ell-1}, t_\ell]\), are piecewise constant over three month periods, \((t_0,t_1],\ (t_1,t_2],\dots,\ (t_7,t_8]\), and follow a seasonal pattern calibrated so we have an average of 50 events on the placebo arm in the first three months, 75 in months 4-6, 50 in months 7-9, and 25 in months 10-12 of the first study year. The baseline hazards in the subsequent study year are halved.

We integrate the hazard and obtain the survival function. Event times can then be simulated via the inverse CDF method. This is facilitated via wrappers implemented in the simsurv package (Brilleman, 2019).

Functions to Simulate COVID-19 Trials

We implement the functions for simulating trials below. Note that these functions will do more than we need in this vignette, but are general purpose wrappers that cover all of the simulations and examples in the manuscript. We first implement a function that returns the cumulative hazard in a time-interval over which the hazards are homogeneous.

# cumulative hazard in a time-homogeneous interval
c_haz_int = 
  function(lambda_t,        # baseline hazard
           t_l,             # left endpoint
           t_r,             # right endpoint
           trt,             # treatment indicator (0 if not yet vaccinated)
           VE_max = NULL,   # VE(0), theta_1
           VE_decay = NULL, # slope parameter, theta_2
           t_trt = NULL,    # vaccination time
           frailty = 1) {
  
  # cumulative hazard over any interval for unvaccinated, always
  if(trt == 0) {
    c_haz = frailty * lambda_t * (t_r - t_l)
  } else {
    if(VE_decay == 0) {
      c_haz = frailty * lambda_t * exp(VE_max) * (t_r - t_l)
    } else {
      c_haz = 
        frailty * lambda_t * exp(VE_max) / VE_decay * 
        (exp(VE_decay * (t_r - t_trt)) - exp(VE_decay * (t_l - t_trt)))
    }
  }
  return(c_haz)
}

We now define a wrapper that calculates the cumulative hazard for a period, (0,t], over which the hazard is time-varying by aggregating the contributions from piecewise-homogeneous intervals.

# cumulative hazard function 
# t: vector of times
# x: matrix with covariates
# betas: vector with parameters
cumul_haz = function(t, x, betas, ...) {
  
  # initialize the hazard vector
  c_haz_t = rep(0.0, length(t))
  
  # get time when hazard starts accumulating
  tstart = max(betas[["t0"]], x[["entry"]])
  
  # baseline hazard intervals
  haz_ints = seq(0, 2.25, by=0.25)
  times = sort(c(unique(c(betas[["t0"]], x[["entry"]], x[["crossover"]],
                          haz_ints, t))))
  endpoints_l = head(times, length(times)-1)
  endpoints_r = tail(times, length(times)-1)
  
  # which intervals are contributing
  contribs = endpoints_l >= tstart & endpoints_r <= min(t, 2.25)
  
  # treatment indicators at left endpoints
  trt_inds = ifelse((x[["trt"]] == 1 & endpoints_l >= x[["entry"]]) |
                      (x[["trt"]] == 0 & endpoints_l >= x[["crossover"]]), 1, 0)
  
  # now compute the cumulative hazards
  for(s in seq_along(t)) {
    
    # initialize vector of cumulative hazards
    c_haz_ints_s = rep(0.0, length(endpoints_l))
    
    # compute the hazards for each interval
    for(i in seq_along(endpoints_l)) {
      if(contribs[i]) {
        
        # grab the baseline hazard
        lambda_t = 
          betas[[paste0("lambda_", 
                        findInterval(endpoints_l[i], 
                                     haz_ints, all.inside = T))]]
        
        # set time of treatment administration
        t_trt = ifelse(x[["trt"]] == 1, x[["entry"]], x[["crossover"]])
        
        # cumulative hazard contribution
        c_haz_ints_s[i] = 
          c_haz_int(lambda_t = lambda_t, 
                    t_l = endpoints_l[i],
                    t_r = endpoints_r[i], 
                    trt = trt_inds[i],
                    VE_max = betas[["VE_max"]],
                    VE_decay = betas[["VE_decay"]],
                    t_trt = t_trt,
                    frailty = x[["frailty"]])
      }
    }
    
    c_haz_t[s] = sum(c_haz_ints_s)
  }
  
  return(c_haz_t)
}

Finally, a wrapper for simulating a COVID-19 vaccine trial.

sim_one <- function(n,                 # number of participants
                    pars,              # vector of simulation parameters
                    cumul_haz,         # cumulative hazard function
                    n_cross,           # number of events to start crossover
                    t_cross,           # time of crossover
                    enrolldur = 12/52, # enrollment period
                    crossdur = 4/52,   # crossover period
                    pvacc = 0.5,       # probability of vaccination
                    frailty_pars = NULL) { # gamma frailty dist params
    
    if(!is.null(t_cross)) {
    
    # create a data frame with subject IDs and treatment indicators
    covars <- data.frame(id = seq_len(n),
                         trt = rbinom(n, 1, pvacc),
                         entry = runif(n, 0, enrolldur),
                         crossover = 0,
                         frailty = 1)
    
    if(!is.null(frailty_pars)) {
      covars$frailty = rgamma(n, shape = frailty_pars[1], rate = frailty_pars[2])
    }
    
    # simulate crossover times for placebo group
    covars$crossover[covars$trt == 0] = 
      t_cross + runif(sum(covars$trt == 0), 1e-5, 1e-5 + crossdur)
    
    # simulate event times
    dat <- simsurv::simsurv(betas = c(pars, t0 = 0), 
                            x = covars,
                            cumhazard = cumul_haz,
                            maxt = 2.25,
                            rootfun = qlogis,
                            ids = covars$id,
                            idvar = "id")
    
    dat <- merge(covars, dat) %>% arrange(eventtime)
    
  } else if(!is.null(n_cross)) {
    
    # create a data frame with subject IDs and treatment indicators
    covars_1 <- data.frame(id = seq_len(n),
                           trt = rbinom(n, 1, pvacc),
                           entry = runif(n, 0, enrolldur),
                           crossover = Inf,
                           frailty = 1)
    
    if(!is.null(frailty_pars)) {
      covars$frailty = rgamma(n, shape = frailty_pars[1], rate = frailty_pars[2])
    }
    
    # simulate event times
    dat_1 <- 
      simsurv::simsurv(betas = c(pars, t0 = 0),
                       x = covars_1,
                       cumhazard = cumul_haz,
                       maxt = 2.25,
                       rootfun = qlogis,
                       ids = covars_1$id,
                       idvar = "id")
    
    # sort by event times
    dat_1 <- dat_1 %>% arrange(eventtime)
    n_events = cumsum(dat_1$status)
    
    # grab the crossover time
    t_cross = dat_1$eventtime[n_events == n_cross][1]
    
    # cache the pre-crossover data
    dat_1 <- dat_1 %>% filter(dat_1$eventtime <= t_cross)
    dat_sim_1 = merge(covars_1, dat_1) %>%  arrange(eventtime)
    
    # subset to get covariates for next part of the simulation
    covars_2 = covars_1[!covars_1$id %in% dat_sim_1$id, ]
    
    # generate crossover times
    covars_2$crossover[covars_2$trt == 0] = 
      t_cross + runif(sum(covars_2$trt == 0), 1e-5, 1e-5 + crossdur)
    
    # keep simulating
    dat_2 <- 
      simsurv::simsurv(betas = c(pars, t0 = t_cross),
                       x = covars_2,
                       cumhazard = cumul_haz,
                       maxt = 2.25,
                       rootfun = qlogis,
                       ids = covars_2$id,
                       idvar = "id")
    
    # sort by event time
    dat_2 <- dat_2 %>% arrange(id)
    
    # merge covars_2 and dat_2
    dat_sim_2 = merge(covars_2, dat_2) %>% arrange(eventtime)
    
    # combine simulated datasets
    dat = rbind(dat_sim_1, dat_sim_2)
    dat = dat %>% arrange(eventtime)  
  }
  
  dat$id = seq_along(dat$id)
  
  # censor people at two years post-study entry
  cens_inds = dat$eventtime > (dat$entry + 2)
  dat$eventtime[cens_inds] = dat$entry[cens_inds] + 2
  dat$status[cens_inds] = 0
  
  return(dat)
}

We will also find it useful to have functions for censoring a trial at crossover and reshaping a simulated dataset to get it into start-stop format.

# to censor people at crossover
cens_cross <- function(dat, n_cross, t_cross) {
    
    if(!is.null(n_cross)) {
        
        # get the crossover time
        t_cross = dat[n_cross, "eventtime"]
        
        # censor events after crossover
        dat$status[(n_cross + 1):nrow(dat)] = 0
        dat$eventtime[(n_cross + 1):nrow(dat)] = t_cross
        
        # get rid of the crossover indicator
        dat$crossover = NULL  
        
    } else {
        
        # get the crossover index
        cross_ind = which(dat[,"eventtime"] > t_cross)[1]
        
        # censor events after crossover
        dat$status[cross_ind:nrow(dat)] = 0
        dat$eventtime[cross_ind:nrow(dat)] = t_cross
        
        # get rid of the crossover indicator
        dat$crossover = NULL
    }
    
    # drop records where people were censored prior to entry
    dat <- subset(dat, eventtime > entry)
    
    # censor people at two years post-study entry
    cens_inds = dat$eventtime > (dat$entry + 2)
    dat$eventtime[cens_inds] = dat$entry[cens_inds] + 2
    dat$status[cens_inds] = 0
    
    # rename columns = 
    names(dat)[1:5] = c("id", "vacc", "tstart", "tstop", "status")
    
    return(dat)
}

reshape_dat <- function(dat, align_entry = FALSE) {
    
    # align times so that entry times correspond to time zero for each participant
    if(align_entry) {
        dat <- 
            dat %>% 
            group_by(id) %>% 
            mutate(crossover = ifelse(trt == 1, 0, crossover - entry),
                   eventtime = eventtime - entry) %>% 
            mutate(entry = 0) %>% 
            ungroup() %>% 
            as.data.frame()
    }
    
    # two rows for each placebo, one for each in the treatment arm
    dat_new <- 
        data.frame(id = unlist(mapply(rep, x = dat$id, 
                                      each = ifelse(dat$trt == 1, 1, 2))),
                   tstart = unlist(lapply(seq_len(nrow(dat)), 
                                          function(x) {
                                              if(dat$trt[x] == 1) {
                                                  dat$entry[x]  
                                              } else {
                                                  c(dat$entry[x], dat$crossover[x])
                                              }})),
                   tstop = NA,
                   status = NA,
                   assg = 0,
                   vacc = 0,
                   tvacc = 0)
    
    # fill out the interval endpoints and status
    tmax = max(dat$eventtime)
    for(s in seq_along(unique(dat_new$id))) {
        
        inds <- which(dat_new$id == dat$id[s])
        
        if(dat$trt[s] == 1) {
            
            dat_new$assg[inds] = 1
            dat_new$vacc[inds] = 1
            dat_new$tvacc[inds] = dat$entry[s]
            dat_new$tstop[inds] = dat$eventtime[s]
            dat_new$status[inds] = dat$status[s]
            
        } else {
            
            dat_new$assg[inds] = c(0,0)
            dat_new$vacc[inds] = c(0,1)
            dat_new$tvacc[inds] = c(dat$crossover[s], dat$crossover[s])
            
            if(dat$eventtime[s] < dat$crossover[s]) {
                
                dat_new$tstop[inds]  = c(dat$eventtime[s], NA)
                dat_new$status[inds] = c(dat$status[s], NA)
                
            } else {
                
                dat_new$tstop[inds] = c(dat$crossover[s], dat$eventtime[s])
                dat_new$status[inds] = c(0, dat$status[s])
            }
        }
    }
    
    dat_new = 
        dat_new[complete.cases(dat_new),] %>% 
        arrange(id, tstop)
    
    return(dat_new)
}

Simulating a COVID-19 Vaccine Trial

Let’s go ahead and simulate a trial. We’ll set the parameters and RNG seed, then simulate a trial. Note again that we are crossing over the placebo arm at 1 year post study initiation and that VE wanes from 85% to 35%, linearly on the log hazard scale, over 1.5 years.

# set up parameters
t_cross = 1    # time of crossover
n_cross = NULL # we're not crossing at some number of events, this is NULL

# To get the baseline hazards
# h = function(r) (pexp(0.5, r) * 1.5e4 - 50)^2
# optimize(h, interval = c(0, 1))

sim_pars_waning = 
    c(VE_max = log(1 - 0.85), # theta_1
      VE_decay = 0.977558,    # theta_2
      lambda_1 = 0.0134,      # 50 / 3 months
      lambda_2 = 0.02,        # 75 / 3 months
      lambda_3 = 0.0134,      # 50 / 3 months
      lambda_4 = 0.0067,      # 25  / 3 months
      lambda_5 = 0.0067,      # 25 / 3 months
      lambda_6 = 0.01,        # 37.5 / 3 months
      lambda_7 = 0.0067,      # 25 / 3 months
      lambda_8 = 0.0033,      # 12.5 / 3 mo
      lambda_9 = 0.0067)      # 25 / 3 mo

# set.seed
set.seed(1834)

# simulate trial
sim_waning <- 
    sim_one(n = 3e4,
            pars = sim_pars_waning, 
            n_cross = n_cross,
            t_cross = t_cross,
            cumul_haz = cumul_haz)

# reshape the simulated dataset
simr_waning <- reshape_dat(sim_waning, align_entry = FALSE)

Here’s what our simulated data looks like. Note that it will be convenient to have vaccination coded as a time-varying covariate, which for the placebo group will change values after the placebo participants are crossed over.

id tstart tstop status assg vacc tvacc
1 0.0137061 0.0165915 1 1 1 0.0137061
2 0.0030863 0.0174004 1 0 0 1.0491566
3 0.0149288 0.0568718 1 0 0 1.0281499
4 0.0305169 0.0643275 1 0 0 1.0725880
5 0.0431431 0.0659803 1 0 0 1.0205335
6 0.0574278 0.0809023 1 0 0 1.0264042
7 0.0573545 0.0912254 1 0 0 1.0395848
8 0.0112373 0.0917694 1 0 0 1.0379315
9 0.0453881 0.0938827 1 0 0 1.0557889
10 0.0988826 0.1003066 1 0 0 1.0564997
11 0.0776694 0.1011311 1 0 0 1.0443900
12 0.0370068 0.1121179 1 0 0 1.0418875
13 0.0138811 0.1347340 1 0 0 1.0767651
14 0.0564214 0.1381631 1 0 0 1.0751959
15 0.0372447 0.1662787 1 0 0 1.0678300
16 0.0732232 0.1720623 1 0 0 1.0163039
17 0.0507713 0.1829451 1 0 0 1.0733530
18 0.0175273 0.1863135 1 0 0 1.0482638
19 0.0161906 0.1979805 1 0 0 1.0205559
20 0.0040547 0.2047842 1 0 0 1.0300624
21 0.2013406 0.2050487 1 0 0 1.0571164
22 0.0470403 0.2221408 1 0 0 1.0417511
23 0.2087467 0.2224980 1 0 0 1.0225845
24 0.0268477 0.2263281 1 0 0 1.0654288
25 0.1635141 0.2288860 1 0 0 1.0029712
26 0.1456497 0.2359233 1 0 0 1.0289817
27 0.0210859 0.2400781 1 1 1 0.0210859
28 0.1607291 0.2470259 1 0 0 1.0411241
29 0.1871308 0.2518624 1 0 0 1.0751910
30 0.1959117 0.2518686 1 0 0 1.0725673
31 0.1717082 0.2521265 1 0 0 1.0432328
32 0.1850362 0.2544609 1 0 0 1.0380911
33 0.1136031 0.2579169 1 0 0 1.0598963
34 0.0849943 0.2590209 1 0 0 1.0419414
35 0.0730949 0.2598562 1 0 0 1.0156556
36 0.1223656 0.2601916 1 1 1 0.1223656
37 0.0903427 0.2638172 1 0 0 1.0272488
38 0.0346006 0.2700530 1 0 0 1.0750477
39 0.0179609 0.2795339 1 1 1 0.0179609
40 0.0136432 0.2799260 1 0 0 1.0063811
41 0.0768189 0.2943987 1 1 1 0.0768189
42 0.1881679 0.2996199 1 1 1 0.1881679
43 0.0985661 0.3010887 1 0 0 1.0199910
44 0.0332535 0.3036390 1 0 0 1.0159256
45 0.0447513 0.3044766 1 0 0 1.0243910
46 0.1057519 0.3066377 1 0 0 1.0210239
47 0.0745494 0.3104922 1 0 0 1.0387453
48 0.2040393 0.3147722 1 0 0 1.0688346
49 0.1870818 0.3156602 1 1 1 0.1870818
50 0.0269703 0.3178789 1 0 0 1.0646517
51 0.1942531 0.3237643 1 0 0 1.0272013
52 0.0439875 0.3258688 1 1 1 0.0439875
53 0.0511368 0.3264467 1 0 0 1.0042030
54 0.1643328 0.3317035 1 0 0 1.0498266
55 0.2288218 0.3322861 1 0 0 1.0074742
56 0.1047753 0.3357087 1 0 0 1.0471680
57 0.1773740 0.3409986 1 0 0 1.0045121
58 0.1547306 0.3414013 1 0 0 1.0304031
59 0.2046110 0.3520256 1 1 1 0.2046110
60 0.1182355 0.3577132 1 0 0 1.0418485
61 0.0642502 0.3638309 1 0 0 1.0527726
62 0.1495354 0.3641997 1 0 0 1.0033787
63 0.1448774 0.3647273 1 0 0 1.0053421
64 0.0014819 0.3692634 1 0 0 1.0306109
65 0.0568324 0.3751098 1 0 0 1.0711791
66 0.1536986 0.3753103 1 0 0 1.0410135
67 0.1825764 0.3758582 1 0 0 1.0317303
68 0.1804050 0.3763175 1 1 1 0.1804050
69 0.0870438 0.3791547 1 0 0 1.0228349
70 0.2157011 0.3799364 1 0 0 1.0204802
71 0.1897332 0.3827875 1 0 0 1.0348277
72 0.1938463 0.3843605 1 0 0 1.0166494
73 0.1666673 0.3904015 1 0 0 1.0269021
74 0.1588192 0.3907617 1 0 0 1.0229891
75 0.0797782 0.3949375 1 0 0 1.0334220
76 0.0041659 0.3977687 1 0 0 1.0095226
77 0.1593631 0.3998857 1 0 0 1.0387372
78 0.0454543 0.4047079 1 1 1 0.0454543
79 0.1874290 0.4082969 1 0 0 1.0239183
80 0.0467313 0.4086130 1 0 0 1.0592943
81 0.0993219 0.4186275 1 0 0 1.0704949
82 0.2018425 0.4186305 1 0 0 1.0450497
83 0.0253175 0.4245824 1 0 0 1.0375605
84 0.0469836 0.4248819 1 0 0 1.0102454
85 0.0959208 0.4249406 1 0 0 1.0153870
86 0.1636318 0.4263720 1 0 0 1.0755812
87 0.1513623 0.4268815 1 0 0 1.0052528
88 0.1808265 0.4289360 1 0 0 1.0600908
89 0.1279179 0.4304230 1 1 1 0.1279179
90 0.2272137 0.4323429 1 0 0 1.0405189
91 0.1573328 0.4399678 1 0 0 1.0257537
92 0.0727711 0.4424535 1 0 0 1.0588347
93 0.1171418 0.4446007 1 0 0 1.0039219
94 0.1354687 0.4450996 1 0 0 1.0417777
95 0.1636735 0.4452727 1 0 0 1.0146297
96 0.1641199 0.4479932 1 0 0 1.0106330
97 0.2097920 0.4482588 1 0 0 1.0661473
98 0.1670534 0.4498800 1 0 0 1.0196379
99 0.1665917 0.4550656 1 0 0 1.0139105
100 0.1365404 0.4551434 1 0 0 1.0263917
101 0.2040099 0.4592289 1 0 0 1.0475243
102 0.1371589 0.4645398 1 0 0 1.0581703
103 0.0230994 0.4661482 1 0 0 1.0084987
104 0.1744820 0.4725203 1 0 0 1.0234292
105 0.2126487 0.4769088 1 0 0 1.0562357
106 0.1912371 0.4773611 1 0 0 1.0177986
107 0.0156501 0.4795458 1 0 0 1.0106221
108 0.1096800 0.4836643 1 0 0 1.0690563
109 0.1059764 0.4848033 1 0 0 1.0766432
110 0.0653074 0.4853547 1 1 1 0.0653074
111 0.1246329 0.4866652 1 0 0 1.0685574
112 0.2110522 0.4871050 1 0 0 1.0640989
113 0.0666658 0.5223218 1 1 1 0.0666658
114 0.1255460 0.5224758 1 1 1 0.1255460
115 0.0979049 0.5341850 1 0 0 1.0202924
116 0.1178426 0.5344129 1 0 0 1.0022401
117 0.1738674 0.5388638 1 0 0 1.0064249
118 0.0077800 0.5429863 1 0 0 1.0061674
119 0.1067071 0.5430124 1 0 0 1.0358997
120 0.1530231 0.5528214 1 0 0 1.0732195
121 0.1991604 0.5646057 1 0 0 1.0199476
122 0.0067009 0.5674759 1 0 0 1.0055030
123 0.0654440 0.5788844 1 0 0 1.0336215
124 0.0605152 0.5806550 1 0 0 1.0472968
125 0.0401674 0.5837007 1 0 0 1.0448361
126 0.2114264 0.5839121 1 0 0 1.0714712
127 0.2032536 0.5862759 1 0 0 1.0488839
128 0.1097839 0.5905932 1 0 0 1.0566629
129 0.0870367 0.5935675 1 0 0 1.0732398
130 0.0867921 0.5974944 1 0 0 1.0497337
131 0.0494009 0.6001562 1 0 0 1.0336013
132 0.0515918 0.6072617 1 0 0 1.0326412
133 0.1934887 0.6097865 1 0 0 1.0021869
134 0.0975281 0.6129537 1 0 0 1.0207479
135 0.1900743 0.6141233 1 1 1 0.1900743
136 0.1636901 0.6144947 1 0 0 1.0443646
137 0.0388095 0.6186908 1 0 0 1.0608338
138 0.1040614 0.6258330 1 0 0 1.0450627
139 0.1711599 0.6264043 1 0 0 1.0149492
140 0.0591485 0.6292358 1 0 0 1.0614610
141 0.2002480 0.6295713 1 0 0 1.0550910
142 0.1006688 0.6376659 1 1 1 0.1006688
143 0.1453988 0.6382029 1 0 0 1.0667979
144 0.2176566 0.6432513 1 0 0 1.0083608
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1699 0.0872197 1.0070292 0 0 0 1.0070292
1699 1.0070292 2.0872197 0 0 1 1.0070292
1700 0.1865615 1.0556275 0 0 0 1.0556275
1700 1.0556275 2.1865615 0 0 1 1.0556275
1701 0.0915897 2.0915897 0 1 1 0.0915897
1702 0.0525353 2.0525353 0 1 1 0.0525353
1703 0.1427665 2.1427665 0 1 1 0.1427665
1704 0.1657419 2.1657419 0 1 1 0.1657419
1705 0.1061682 1.0705754 0 0 0 1.0705754
1705 1.0705754 2.1061682 0 0 1 1.0705754
1706 0.0114545 1.0705021 0 0 0 1.0705021
1706 1.0705021 2.0114545 0 0 1 1.0705021
1707 0.0413559 2.0413559 0 1 1 0.0413559
1708 0.1143567 2.1143567 0 1 1 0.1143567
1709 0.2225971 1.0757680 0 0 0 1.0757680
1709 1.0757680 2.2225971 0 0 1 1.0757680
1710 0.2174595 1.0417980 0 0 0 1.0417980
1710 1.0417980 2.2174595 0 0 1 1.0417980
1711 0.0155224 1.0286714 0 0 0 1.0286714
1711 1.0286714 2.0155224 0 0 1 1.0286714
1712 0.1666214 2.1666214 0 1 1 0.1666214
1713 0.1758474 1.0219665 0 0 0 1.0219665
1713 1.0219665 2.1758474 0 0 1 1.0219665
1714 0.0447890 2.0447890 0 1 1 0.0447890
1715 0.0180073 2.0180073 0 1 1 0.0180073
1716 0.0922683 1.0364400 0 0 0 1.0364400
1716 1.0364400 2.0922683 0 0 1 1.0364400
1717 0.1375336 2.1375336 0 1 1 0.1375336
1718 0.0251883 2.0251883 0 1 1 0.0251883
1719 0.1857912 1.0273536 0 0 0 1.0273536
1719 1.0273536 2.1857912 0 0 1 1.0273536
1720 0.1803649 1.0404886 0 0 0 1.0404886
1720 1.0404886 2.1803649 0 0 1 1.0404886
1721 0.2219643 2.2219643 0 1 1 0.2219643
1722 0.1956735 2.1956735 0 1 1 0.1956735
1723 0.1529619 1.0517729 0 0 0 1.0517729
1723 1.0517729 2.1529619 0 0 1 1.0517729
1724 0.0176463 1.0753647 0 0 0 1.0753647
1724 1.0753647 2.0176463 0 0 1 1.0753647
1725 0.0788614 1.0706287 0 0 0 1.0706287
1725 1.0706287 2.0788614 0 0 1 1.0706287
1726 0.2287539 2.2287539 0 1 1 0.2287539
1727 0.1353846 1.0611280 0 0 0 1.0611280
1727 1.0611280 2.1353846 0 0 1 1.0611280
1728 0.0385531 2.0385531 0 1 1 0.0385531
1729 0.1839504 1.0479837 0 0 0 1.0479837
1729 1.0479837 2.1839504 0 0 1 1.0479837
1730 0.0882729 2.0882729 0 1 1 0.0882729
1731 0.1725277 1.0469633 0 0 0 1.0469633
1731 1.0469633 2.1725277 0 0 1 1.0469633
1732 0.0156362 1.0639134 0 0 0 1.0639134
1732 1.0639134 2.0156362 0 0 1 1.0639134
1733 0.1378224 2.1378224 0 1 1 0.1378224
1734 0.1823337 2.1823337 0 1 1 0.1823337
1735 0.1800229 2.1800229 0 1 1 0.1800229
1736 0.1301391 2.1301391 0 1 1 0.1301391
1737 0.2192118 2.2192118 0 1 1 0.2192118
1738 0.0397409 1.0157227 0 0 0 1.0157227
1738 1.0157227 2.0397409 0 0 1 1.0157227
1739 0.1921092 2.1921092 0 1 1 0.1921092
1740 0.0054666 1.0399651 0 0 0 1.0399651
1740 1.0399651 2.0054666 0 0 1 1.0399651
1741 0.0938462 2.0938462 0 1 1 0.0938462
1742 0.0560057 2.0560057 0 1 1 0.0560057
1743 0.0901765 1.0433246 0 0 0 1.0433246
1743 1.0433246 2.0901765 0 0 1 1.0433246
1744 0.0148860 1.0255441 0 0 0 1.0255441
1744 1.0255441 2.0148860 0 0 1 1.0255441
1745 0.1849658 2.1849658 0 1 1 0.1849658
1746 0.0261351 1.0270243 0 0 0 1.0270243
1746 1.0270243 2.0261351 0 0 1 1.0270243
1747 0.0716552 2.0716552 0 1 1 0.0716552
1748 0.2186924 1.0179512 0 0 0 1.0179512
1748 1.0179512 2.2186924 0 0 1 1.0179512
1749 0.2256684 2.2256684 0 1 1 0.2256684
1750 0.1693006 2.1693006 0 1 1 0.1693006
1751 0.0266411 2.0266411 0 1 1 0.0266411
1752 0.1744837 1.0396621 0 0 0 1.0396621
1752 1.0396621 2.1744837 0 0 1 1.0396621
1753 0.0948919 1.0378388 0 0 0 1.0378388
1753 1.0378388 2.0948919 0 0 1 1.0378388
1754 0.1305379 1.0051311 0 0 0 1.0051311
1754 1.0051311 2.1305379 0 0 1 1.0051311
1755 0.1829659 2.1829659 0 1 1 0.1829659
1756 0.1803884 1.0587313 0 0 0 1.0587313
1756 1.0587313 2.1803884 0 0 1 1.0587313
1757 0.1717799 1.0324306 0 0 0 1.0324306
1757 1.0324306 2.1717799 0 0 1 1.0324306
1758 0.2125052 1.0342305 0 0 0 1.0342305
1758 1.0342305 2.2125052 0 0 1 1.0342305
1759 0.1401676 1.0021450 0 0 0 1.0021450
1759 1.0021450 2.1401676 0 0 1 1.0021450
1760 0.0353830 1.0569379 0 0 0 1.0569379
1760 1.0569379 2.0353830 0 0 1 1.0569379
1761 0.0970056 1.0288398 0 0 0 1.0288398
1761 1.0288398 2.0970056 0 0 1 1.0288398
1762 0.0003334 2.0003334 0 1 1 0.0003334
1763 0.2002030 2.2002030 0 1 1 0.2002030
1764 0.0174112 2.0174112 0 1 1 0.0174112
1765 0.1714548 1.0758100 0 0 0 1.0758100
1765 1.0758100 2.1714548 0 0 1 1.0758100
1766 0.2264621 2.2264621 0 1 1 0.2264621
1767 0.1984855 1.0125153 0 0 0 1.0125153
1767 1.0125153 2.1984855 0 0 1 1.0125153
1768 0.0686673 1.0696925 0 0 0 1.0696925
1768 1.0696925 2.0686673 0 0 1 1.0696925
1769 0.0994808 2.0994808 0 1 1 0.0994808
1770 0.1122091 1.0268126 0 0 0 1.0268126
1770 1.0268126 2.1122091 0 0 1 1.0268126
1771 0.1410648 1.0751818 0 0 0 1.0751818
1771 1.0751818 2.1410648 0 0 1 1.0751818
1772 0.0335883 1.0129413 0 0 0 1.0129413
1772 1.0129413 2.0335883 0 0 1 1.0129413
1773 0.0296887 2.0296887 0 1 1 0.0296887
1774 0.1381102 2.1381102 0 1 1 0.1381102
1775 0.2000096 1.0212939 0 0 0 1.0212939
1775 1.0212939 2.2000096 0 0 1 1.0212939
1776 0.0166514 2.0166514 0 1 1 0.0166514
1777 0.1422793 1.0178773 0 0 0 1.0178773
1777 1.0178773 2.1422793 0 0 1 1.0178773
1778 0.2151042 2.2151042 0 1 1 0.2151042
1779 0.1063935 1.0178664 0 0 0 1.0178664
1779 1.0178664 2.1063935 0 0 1 1.0178664
1780 0.1707429 1.0228010 0 0 0 1.0228010
1780 1.0228010 2.1707429 0 0 1 1.0228010
1781 0.0879564 2.0879564 0 1 1 0.0879564
1782 0.1084075 2.1084075 0 1 1 0.1084075
1783 0.1769357 2.1769357 0 1 1 0.1769357
1784 0.2303986 2.2303986 0 1 1 0.2303986
1785 0.1976417 1.0066156 0 0 0 1.0066156
1785 1.0066156 2.1976417 0 0 1 1.0066156
1786 0.1009917 2.1009917 0 1 1 0.1009917
1787 0.0792673 2.0792673 0 1 1 0.0792673
1788 0.0603647 1.0649119 0 0 0 1.0649119
1788 1.0649119 2.0603647 0 0 1 1.0649119
1789 0.1652796 1.0129809 0 0 0 1.0129809
1789 1.0129809 2.1652796 0 0 1 1.0129809
1790 0.0189387 2.0189387 0 1 1 0.0189387
1791 0.1967275 1.0708501 0 0 0 1.0708501
1791 1.0708501 2.1967275 0 0 1 1.0708501
1792 0.1457097 2.1457097 0 1 1 0.1457097
1793 0.1246785 2.1246785 0 1 1 0.1246785
1794 0.1008215 1.0035571 0 0 0 1.0035571
1794 1.0035571 2.1008215 0 0 1 1.0035571
1795 0.1170388 2.1170388 0 1 1 0.1170388
1796 0.1059837 1.0402847 0 0 0 1.0402847
1796 1.0402847 2.1059837 0 0 1 1.0402847
1797 0.0246639 1.0711550 0 0 0 1.0711550
1797 1.0711550 2.0246639 0 0 1 1.0711550
1798 0.1196523 1.0024549 0 0 0 1.0024549
1798 1.0024549 2.1196523 0 0 1 1.0024549
1799 0.1852544 2.1852544 0 1 1 0.1852544
1800 0.0447238 1.0101207 0 0 0 1.0101207
1800 1.0101207 2.0447238 0 0 1 1.0101207
1801 0.0328665 1.0026685 0 0 0 1.0026685
1801 1.0026685 2.0328665 0 0 1 1.0026685
1802 0.0136934 2.0136934 0 1 1 0.0136934
1803 0.2265651 2.2265651 0 1 1 0.2265651
1804 0.1321343 1.0122584 0 0 0 1.0122584
1804 1.0122584 2.1321343 0 0 1 1.0122584
1805 0.1247846 2.1247846 0 1 1 0.1247846
1806 0.2004539 1.0118580 0 0 0 1.0118580
1806 1.0118580 2.2004539 0 0 1 1.0118580
1807 0.1715795 2.1715795 0 1 1 0.1715795
1808 0.0110925 2.0110925 0 1 1 0.0110925
1809 0.1543991 2.1543991 0 1 1 0.1543991
1810 0.0167155 1.0752864 0 0 0 1.0752864
1810 1.0752864 2.0167155 0 0 1 1.0752864
1811 0.2226046 2.2226046 0 1 1 0.2226046
1812 0.1216700 1.0336914 0 0 0 1.0336914
1812 1.0336914 2.1216700 0 0 1 1.0336914
1813 0.1568612 1.0629241 0 0 0 1.0629241
1813 1.0629241 2.1568612 0 0 1 1.0629241
1814 0.1262552 2.1262552 0 1 1 0.1262552
1815 0.2263694 1.0241818 0 0 0 1.0241818
1815 1.0241818 2.2263694 0 0 1 1.0241818
1816 0.0328117 2.0328117 0 1 1 0.0328117
1817 0.1130814 2.1130814 0 1 1 0.1130814
1818 0.0402831 2.0402831 0 1 1 0.0402831
1819 0.1600053 2.1600053 0 1 1 0.1600053
1820 0.0915380 2.0915380 0 1 1 0.0915380
1821 0.0043984 2.0043984 0 1 1 0.0043984
1822 0.1519094 2.1519094 0 1 1 0.1519094
1823 0.0776384 2.0776384 0 1 1 0.0776384
1824 0.1417685 2.1417685 0 1 1 0.1417685
1825 0.0284267 1.0242822 0 0 0 1.0242822
1825 1.0242822 2.0284267 0 0 1 1.0242822
1826 0.1653218 2.1653218 0 1 1 0.1653218
1827 0.1849694 1.0213886 0 0 0 1.0213886
1827 1.0213886 2.1849694 0 0 1 1.0213886
1828 0.1912650 1.0111820 0 0 0 1.0111820
1828 1.0111820 2.1912650 0 0 1 1.0111820
1829 0.0785339 2.0785339 0 1 1 0.0785339
1830 0.1433914 1.0143025 0 0 0 1.0143025
1830 1.0143025 2.1433914 0 0 1 1.0143025
1831 0.2169253 2.2169253 0 1 1 0.2169253
1832 0.2030050 1.0485860 0 0 0 1.0485860
1832 1.0485860 2.2030050 0 0 1 1.0485860
1833 0.0356891 1.0670764 0 0 0 1.0670764
1833 1.0670764 2.0356891 0 0 1 1.0670764
1834 0.0880609 2.0880609 0 1 1 0.0880609
1835 0.2304041 2.2304041 0 1 1 0.2304041
1836 0.1991471 2.1991471 0 1 1 0.1991471
1837 0.0089079 2.0089079 0 1 1 0.0089079
1838 0.1913954 1.0310274 0 0 0 1.0310274
1838 1.0310274 2.1913954 0 0 1 1.0310274
1839 0.0256189 1.0115319 0 0 0 1.0115319
1839 1.0115319 2.0256189 0 0 1 1.0115319
1840 0.0895232 1.0715736 0 0 0 1.0715736
1840 1.0715736 2.0895232 0 0 1 1.0715736
1841 0.1588524 1.0086397 0 0 0 1.0086397
1841 1.0086397 2.1588524 0 0 1 1.0086397
1842 0.0949738 1.0697261 0 0 0 1.0697261
1842 1.0697261 2.0949738 0 0 1 1.0697261
1843 0.0245928 2.0245928 0 1 1 0.0245928
1844 0.0409514 1.0049879 0 0 0 1.0049879
1844 1.0049879 2.0409514 0 0 1 1.0049879
1845 0.1757284 1.0451881 0 0 0 1.0451881
1845 1.0451881 2.1757284 0 0 1 1.0451881
1846 0.1477124 1.0489261 0 0 0 1.0489261
1846 1.0489261 2.1477124 0 0 1 1.0489261
1847 0.0475043 1.0652931 0 0 0 1.0652931
1847 1.0652931 2.0475043 0 0 1 1.0652931
1848 0.1310845 2.1310845 0 1 1 0.1310845
1849 0.0603391 1.0460399 0 0 0 1.0460399
1849 1.0460399 2.0603391 0 0 1 1.0460399
1850 0.1774112 2.1774112 0 1 1 0.1774112
1851 0.0625253 1.0201208 0 0 0 1.0201208
1851 1.0201208 2.0625253 0 0 1 1.0201208
1852 0.0736577 1.0696592 0 0 0 1.0696592
1852 1.0696592 2.0736577 0 0 1 1.0696592
1853 0.0095920 2.0095920 0 1 1 0.0095920
1854 0.0893912 1.0073386 0 0 0 1.0073386
1854 1.0073386 2.0893912 0 0 1 1.0073386
1855 0.0850730 2.0850730 0 1 1 0.0850730
1856 0.1696089 2.1696089 0 1 1 0.1696089
1857 0.1013546 2.1013546 0 1 1 0.1013546
1858 0.0119289 2.0119289 0 1 1 0.0119289
1859 0.0391309 1.0461895 0 0 0 1.0461895
1859 1.0461895 2.0391309 0 0 1 1.0461895
1860 0.0541974 1.0148621 0 0 0 1.0148621
1860 1.0148621 2.0541974 0 0 1 1.0148621
1861 0.1097110 1.0698895 0 0 0 1.0698895
1861 1.0698895 2.1097110 0 0 1 1.0698895
1862 0.0303085 1.0478941 0 0 0 1.0478941
1862 1.0478941 2.0303085 0 0 1 1.0478941
1863 0.1757590 2.1757590 0 1 1 0.1757590
1864 0.2191694 2.2191694 0 1 1 0.2191694
1865 0.0716847 2.0716847 0 1 1 0.0716847
1866 0.0003840 1.0711679 0 0 0 1.0711679
1866 1.0711679 2.0003840 0 0 1 1.0711679
1867 0.0132990 1.0732414 0 0 0 1.0732414
1867 1.0732414 2.0132990 0 0 1 1.0732414
1868 0.1782450 2.1782450 0 1 1 0.1782450
1869 0.1824123 2.1824123 0 1 1 0.1824123
1870 0.0008461 2.0008461 0 1 1 0.0008461
1871 0.0655382 2.0655382 0 1 1 0.0655382
1872 0.1729278 1.0573506 0 0 0 1.0573506
1872 1.0573506 2.1729278 0 0 1 1.0573506
1873 0.0347219 1.0757299 0 0 0 1.0757299
1873 1.0757299 2.0347219 0 0 1 1.0757299
1874 0.0432504 1.0753995 0 0 0 1.0753995
1874 1.0753995 2.0432504 0 0 1 1.0753995
1875 0.1963387 2.1963387 0 1 1 0.1963387
1876 0.2199525 1.0529141 0 0 0 1.0529141
1876 1.0529141 2.2199525 0 0 1 1.0529141
1877 0.0570225 2.0570225 0 1 1 0.0570225
1878 0.1984171 1.0662298 0 0 0 1.0662298
1878 1.0662298 2.1984171 0 0 1 1.0662298
1879 0.1869646 1.0005076 0 0 0 1.0005076
1879 1.0005076 2.1869646 0 0 1 1.0005076
1880 0.0179968 2.0179968 0 1 1 0.0179968
1881 0.0232136 1.0011654 0 0 0 1.0011654
1881 1.0011654 2.0232136 0 0 1 1.0011654
1882 0.1091123 1.0161412 0 0 0 1.0161412
1882 1.0161412 2.1091123 0 0 1 1.0161412
1883 0.0512121 2.0512121 0 1 1 0.0512121
1884 0.2265505 1.0290246 0 0 0 1.0290246
1884 1.0290246 2.2265505 0 0 1 1.0290246
1885 0.1049568 2.1049568 0 1 1 0.1049568
1886 0.1290880 2.1290880 0 1 1 0.1290880
1887 0.1924559 1.0713843 0 0 0 1.0713843
1887 1.0713843 2.1924559 0 0 1 1.0713843
1888 0.2067520 2.2067520 0 1 1 0.2067520
1889 0.0509759 1.0372928 0 0 0 1.0372928
1889 1.0372928 2.0509759 0 0 1 1.0372928
1890 0.1913004 1.0591961 0 0 0 1.0591961
1890 1.0591961 2.1913004 0 0 1 1.0591961
1891 0.0934834 2.0934834 0 1 1 0.0934834
1892 0.2298447 2.2298447 0 1 1 0.2298447
1893 0.2102339 2.2102339 0 1 1 0.2102339
1894 0.1614369 2.1614369 0 1 1 0.1614369
1895 0.2150221 2.2150221 0 1 1 0.2150221
1896 0.1012182 2.1012182 0 1 1 0.1012182
1897 0.1220690 1.0179571 0 0 0 1.0179571
1897 1.0179571 2.1220690 0 0 1 1.0179571
1898 0.0153156 1.0515028 0 0 0 1.0515028
1898 1.0515028 2.0153156 0 0 1 1.0515028
1899 0.1886745 1.0542403 0 0 0 1.0542403
1899 1.0542403 2.1886745 0 0 1 1.0542403
1900 0.0260008 1.0639337 0 0 0 1.0639337
1900 1.0639337 2.0260008 0 0 1 1.0639337
1901 0.1202642 2.1202642 0 1 1 0.1202642
1902 0.1808586 2.1808586 0 1 1 0.1808586
1903 0.1565687 1.0682890 0 0 0 1.0682890
1903 1.0682890 2.1565687 0 0 1 1.0682890
1904 0.1120412 2.1120412 0 1 1 0.1120412
1905 0.2272136 2.2272136 0 1 1 0.2272136
1906 0.1349379 2.1349379 0 1 1 0.1349379
1907 0.0138846 2.0138846 0 1 1 0.0138846
1908 0.1880775 1.0298679 0 0 0 1.0298679
1908 1.0298679 2.1880775 0 0 1 1.0298679
1909 0.0595115 1.0650713 0 0 0 1.0650713
1909 1.0650713 2.0595115 0 0 1 1.0650713
1910 0.1065606 2.1065606 0 1 1 0.1065606
1911 0.0547261 2.0547261 0 1 1 0.0547261
1912 0.0453094 2.0453094 0 1 1 0.0453094
1913 0.0901271 2.0901271 0 1 1 0.0901271
1914 0.2086619 1.0168514 0 0 0 1.0168514
1914 1.0168514 2.2086619 0 0 1 1.0168514
1915 0.2271734 2.2271734 0 1 1 0.2271734
1916 0.1579499 2.1579499 0 1 1 0.1579499
1917 0.2221725 1.0213255 0 0 0 1.0213255
1917 1.0213255 2.2221725 0 0 1 1.0213255
1918 0.0692069 2.0692069 0 1 1 0.0692069
1919 0.1637911 1.0178531 0 0 0 1.0178531
1919 1.0178531 2.1637911 0 0 1 1.0178531
1920 0.1922957 2.1922957 0 1 1 0.1922957
1921 0.1491758 2.1491758 0 1 1 0.1491758
1922 0.1975489 1.0586785 0 0 0 1.0586785
1922 1.0586785 2.1975489 0 0 1 1.0586785
1923 0.1366542 2.1366542 0 1 1 0.1366542
1924 0.1077223 2.1077223 0 1 1 0.1077223
1925 0.0957969 1.0176749 0 0 0 1.0176749
1925 1.0176749 2.0957969 0 0 1 1.0176749
1926 0.1531738 2.1531738 0 1 1 0.1531738
1927 0.1974367 2.1974367 0 1 1 0.1974367
1928 0.0087408 1.0169054 0 0 0 1.0169054
1928 1.0169054 2.0087408 0 0 1 1.0169054
1929 0.1762297 1.0191768 0 0 0 1.0191768
1929 1.0191768 2.1762297 0 0 1 1.0191768
1930 0.1260384 1.0629362 0 0 0 1.0629362
1930 1.0629362 2.1260384 0 0 1 1.0629362
1931 0.0508800 2.0508800 0 1 1 0.0508800
1932 0.0289881 1.0455769 0 0 0 1.0455769
1932 1.0455769 2.0289881 0 0 1 1.0455769
1933 0.1988999 2.1988999 0 1 1 0.1988999
1934 0.2164677 1.0684638 0 0 0 1.0684638
1934 1.0684638 2.2164677 0 0 1 1.0684638
1935 0.0319946 2.0319946 0 1 1 0.0319946
1936 0.1334019 2.1334019 0 1 1 0.1334019
1937 0.2089292 1.0003637 0 0 0 1.0003637
1937 1.0003637 2.2089292 0 0 1 1.0003637
1938 0.1701874 2.1701874 0 1 1 0.1701874
1939 0.1563321 1.0244554 0 0 0 1.0244554
1939 1.0244554 2.1563321 0 0 1 1.0244554
1940 0.1684823 2.1684823 0 1 1 0.1684823
1941 0.1193842 1.0437674 0 0 0 1.0437674
1941 1.0437674 2.1193842 0 0 1 1.0437674
1942 0.0306636 2.0306636 0 1 1 0.0306636
1943 0.0727017 2.0727017 0 1 1 0.0727017
1944 0.1280174 1.0435026 0 0 0 1.0435026
1944 1.0435026 2.1280174 0 0 1 1.0435026
1945 0.0247052 2.0247052 0 1 1 0.0247052
1946 0.0290278 2.0290278 0 1 1 0.0290278
1947 0.1445683 2.1445683 0 1 1 0.1445683
1948 0.1066840 2.1066840 0 1 1 0.1066840
1949 0.1774692 1.0397036 0 0 0 1.0397036
1949 1.0397036 2.1774692 0 0 1 1.0397036
1950 0.0463264 1.0765251 0 0 0 1.0765251
1950 1.0765251 2.0463264 0 0 1 1.0765251
1951 0.0365320 2.0365320 0 1 1 0.0365320
1952 0.0849924 2.0849924 0 1 1 0.0849924
1953 0.0328639 2.0328639 0 1 1 0.0328639
1954 0.0467389 1.0157380 0 0 0 1.0157380
1954 1.0157380 2.0467389 0 0 1 1.0157380
1955 0.2277207 2.2277207 0 1 1 0.2277207
1956 0.0418202 1.0222138 0 0 0 1.0222138
1956 1.0222138 2.0418202 0 0 1 1.0222138
1957 0.0322668 1.0436997 0 0 0 1.0436997
1957 1.0436997 2.0322668 0 0 1 1.0436997
1958 0.0036046 1.0723476 0 0 0 1.0723476
1958 1.0723476 2.0036046 0 0 1 1.0723476
1959 0.1178575 1.0096966 0 0 0 1.0096966
1959 1.0096966 2.1178575 0 0 1 1.0096966
1960 0.1557802 2.1557802 0 1 1 0.1557802
1961 0.1948893 1.0760502 0 0 0 1.0760502
1961 1.0760502 2.1948893 0 0 1 1.0760502
1962 0.1373537 2.1373537 0 1 1 0.1373537
1963 0.1971317 2.1971317 0 1 1 0.1971317
1964 0.1712642 2.1712642 0 1 1 0.1712642
1965 0.0791934 2.0791934 0 1 1 0.0791934
1966 0.0303195 2.0303195 0 1 1 0.0303195
1967 0.1834661 2.1834661 0 1 1 0.1834661
1968 0.1423025 1.0754965 0 0 0 1.0754965
1968 1.0754965 2.1423025 0 0 1 1.0754965
1969 0.0598152 1.0289374 0 0 0 1.0289374
1969 1.0289374 2.0598152 0 0 1 1.0289374
1970 0.1515411 1.0478413 0 0 0 1.0478413
1970 1.0478413 2.1515411 0 0 1 1.0478413
1971 0.0778092 1.0286744 0 0 0 1.0286744
1971 1.0286744 2.0778092 0 0 1 1.0286744
1972 0.0794247 2.0794247 0 1 1 0.0794247
1973 0.0468076 2.0468076 0 1 1 0.0468076
1974 0.1416912 1.0644335 0 0 0 1.0644335
1974 1.0644335 2.1416912 0 0 1 1.0644335
1975 0.1393940 2.1393940 0 1 1 0.1393940
1976 0.2270141 2.2270141 0 1 1 0.2270141
1977 0.0011310 1.0006156 0 0 0 1.0006156
1977 1.0006156 2.0011310 0 0 1 1.0006156
1978 0.1149057 1.0696576 0 0 0 1.0696576
1978 1.0696576 2.1149057 0 0 1 1.0696576
1979 0.2109841 2.2109841 0 1 1 0.2109841
1980 0.2060246 1.0081958 0 0 0 1.0081958
1980 1.0081958 2.2060246 0 0 1 1.0081958
1981 0.0195025 2.0195025 0 1 1 0.0195025
1982 0.1643203 1.0095273 0 0 0 1.0095273
1982 1.0095273 2.1643203 0 0 1 1.0095273
1983 0.1985234 1.0256731 0 0 0 1.0256731
1983 1.0256731 2.1985234 0 0 1 1.0256731
1984 0.2107321 2.2107321 0 1 1 0.2107321
1985 0.0859909 1.0392267 0 0 0 1.0392267
1985 1.0392267 2.0859909 0 0 1 1.0392267
1986 0.1380181 1.0273276 0 0 0 1.0273276
1986 1.0273276 2.1380181 0 0 1 1.0273276
1987 0.1493896 1.0692500 0 0 0 1.0692500
1987 1.0692500 2.1493896 0 0 1 1.0692500
1988 0.0372345 1.0452248 0 0 0 1.0452248
1988 1.0452248 2.0372345 0 0 1 1.0452248
1989 0.0895296 2.0895296 0 1 1 0.0895296
1990 0.0812624 2.0812624 0 1 1 0.0812624
1991 0.0559522 1.0244472 0 0 0 1.0244472
1991 1.0244472 2.0559522 0 0 1 1.0244472
1992 0.2030877 2.2030877 0 1 1 0.2030877
1993 0.0593076 2.0593076 0 1 1 0.0593076
1994 0.1150013 1.0687630 0 0 0 1.0687630
1994 1.0687630 2.1150013 0 0 1 1.0687630
1995 0.0273939 2.0273939 0 1 1 0.0273939
1996 0.1771452 1.0754472 0 0 0 1.0754472
1996 1.0754472 2.1771452 0 0 1 1.0754472
1997 0.0854275 2.0854275 0 1 1 0.0854275
1998 0.2055119 2.2055119 0 1 1 0.2055119
1999 0.0562784 1.0199018 0 0 0 1.0199018
1999 1.0199018 2.0562784 0 0 1 1.0199018
2000 0.0925089 2.0925089 0 1 1 0.0925089
2001 0.0709256 1.0298213 0 0 0 1.0298213
2001 1.0298213 2.0709256 0 0 1 1.0298213
2002 0.1798274 2.1798274 0 1 1 0.1798274
2003 0.1280937 1.0244535 0 0 0 1.0244535
2003 1.0244535 2.1280937 0 0 1 1.0244535
2004 0.0166573 1.0415200 0 0 0 1.0415200
2004 1.0415200 2.0166573 0 0 1 1.0415200
2005 0.0848396 2.0848396 0 1 1 0.0848396
2006 0.1955822 1.0064389 0 0 0 1.0064389
2006 1.0064389 2.1955822 0 0 1 1.0064389
2007 0.0856701 1.0320190 0 0 0 1.0320190
2007 1.0320190 2.0856701 0 0 1 1.0320190
2008 0.1717471 2.1717471 0 1 1 0.1717471
2009 0.0256041 2.0256041 0 1 1 0.0256041
2010 0.1534768 1.0643258 0 0 0 1.0643258
2010 1.0643258 2.1534768 0 0 1 1.0643258
2011 0.0283214 1.0516075 0 0 0 1.0516075
2011 1.0516075 2.0283214 0 0 1 1.0516075
2012 0.1930839 1.0325988 0 0 0 1.0325988
2012 1.0325988 2.1930839 0 0 1 1.0325988
2013 0.0501811 1.0302882 0 0 0 1.0302882
2013 1.0302882 2.0501811 0 0 1 1.0302882
2014 0.1206855 1.0508322 0 0 0 1.0508322
2014 1.0508322 2.1206855 0 0 1 1.0508322
2015 0.0963200 2.0963200 0 1 1 0.0963200
2016 0.1858767 2.1858767 0 1 1 0.1858767
2017 0.0939163 2.0939163 0 1 1 0.0939163
2018 0.2062240 2.2062240 0 1 1 0.2062240
2019 0.2064268 1.0225933 0 0 0 1.0225933
2019 1.0225933 2.2064268 0 0 1 1.0225933
2020 0.2130714 2.2130714 0 1 1 0.2130714
2021 0.0067024 2.0067024 0 1 1 0.0067024
2022 0.0450138 1.0154786 0 0 0 1.0154786
2022 1.0154786 2.0450138 0 0 1 1.0154786
2023 0.1898177 2.1898177 0 1 1 0.1898177
2024 0.1041678 2.1041678 0 1 1 0.1041678
2025 0.2063046 1.0084559 0 0 0 1.0084559
2025 1.0084559 2.2063046 0 0 1 1.0084559
2026 0.1721073 2.1721073 0 1 1 0.1721073
2027 0.1034900 2.1034900 0 1 1 0.1034900
2028 0.2196056 1.0290935 0 0 0 1.0290935
2028 1.0290935 2.2196056 0 0 1 1.0290935
2029 0.1256635 2.1256635 0 1 1 0.1256635
2030 0.1004701 1.0112608 0 0 0 1.0112608
2030 1.0112608 2.1004701 0 0 1 1.0112608
2031 0.0741609 1.0545457 0 0 0 1.0545457
2031 1.0545457 2.0741609 0 0 1 1.0545457
2032 0.1563496 2.1563496 0 1 1 0.1563496
2033 0.0890889 2.0890889 0 1 1 0.0890889
2034 0.0393121 2.0393121 0 1 1 0.0393121
2035 0.1854547 2.1854547 0 1 1 0.1854547
2036 0.1564171 1.0759347 0 0 0 1.0759347
2036 1.0759347 2.1564171 0 0 1 1.0759347
2037 0.0238841 1.0634428 0 0 0 1.0634428
2037 1.0634428 2.0238841 0 0 1 1.0634428
2038 0.1568664 2.1568664 0 1 1 0.1568664
2039 0.2253943 1.0225195 0 0 0 1.0225195
2039 1.0225195 2.2253943 0 0 1 1.0225195
2040 0.1036087 1.0653144 0 0 0 1.0653144
2040 1.0653144 2.1036087 0 0 1 1.0653144
2041 0.1496650 2.1496650 0 1 1 0.1496650
2042 0.0014022 2.0014022 0 1 1 0.0014022
2043 0.1591679 1.0233438 0 0 0 1.0233438
2043 1.0233438 2.1591679 0 0 1 1.0233438
2044 0.2064147 2.2064147 0 1 1 0.2064147
2045 0.0373769 1.0250236 0 0 0 1.0250236
2045 1.0250236 2.0373769 0 0 1 1.0250236
2046 0.0317419 1.0505032 0 0 0 1.0505032
2046 1.0505032 2.0317419 0 0 1 1.0505032
2047 0.1735927 1.0368978 0 0 0 1.0368978
2047 1.0368978 2.1735927 0 0 1 1.0368978
2048 0.2095377 1.0462243 0 0 0 1.0462243
2048 1.0462243 2.2095377 0 0 1 1.0462243
2049 0.1162488 2.1162488 0 1 1 0.1162488
2050 0.0473527 2.0473527 0 1 1 0.0473527
2051 0.0672943 2.0672943 0 1 1 0.0672943
2052 0.0302719 1.0628420 0 0 0 1.0628420
2052 1.0628420 2.0302719 0 0 1 1.0628420
2053 0.0281645 2.0281645 0 1 1 0.0281645
2054 0.0685857 2.0685857 0 1 1 0.0685857
2055 0.1418325 1.0461982 0 0 0 1.0461982
2055 1.0461982 2.1418325 0 0 1 1.0461982
2056 0.1361809 1.0354474 0 0 0 1.0354474
2056 1.0354474 2.1361809 0 0 1 1.0354474
2057 0.0281744 2.0281744 0 1 1 0.0281744
2058 0.0649361 2.0649361 0 1 1 0.0649361
2059 0.1920841 1.0022419 0 0 0 1.0022419
2059 1.0022419 2.1920841 0 0 1 1.0022419
2060 0.1729705 1.0200412 0 0 0 1.0200412
2060 1.0200412 2.1729705 0 0 1 1.0200412
2061 0.1639911 2.1639911 0 1 1 0.1639911
2062 0.0995673 2.0995673 0 1 1 0.0995673
2063 0.0890595 1.0078065 0 0 0 1.0078065
2063 1.0078065 2.0890595 0 0 1 1.0078065
2064 0.1588505 1.0053468 0 0 0 1.0053468
2064 1.0053468 2.1588505 0 0 1 1.0053468
2065 0.2143314 2.2143314 0 1 1 0.2143314
2066 0.0842211 2.0842211 0 1 1 0.0842211
2067 0.1225990 2.1225990 0 1 1 0.1225990
2068 0.2076942 2.2076942 0 1 1 0.2076942
2069 0.0083619 1.0602977 0 0 0 1.0602977
2069 1.0602977 2.0083619 0 0 1 1.0602977
2070 0.0835461 2.0835461 0 1 1 0.0835461
2071 0.1426101 1.0493320 0 0 0 1.0493320
2071 1.0493320 2.1426101 0 0 1 1.0493320
2072 0.1790119 2.1790119 0 1 1 0.1790119
2073 0.0687051 2.0687051 0 1 1 0.0687051
2074 0.0099023 2.0099023 0 1 1 0.0099023
2075 0.1702986 2.1702986 0 1 1 0.1702986
2076 0.1078783 2.1078783 0 1 1 0.1078783
2077 0.0893354 2.0893354 0 1 1 0.0893354
2078 0.1853284 1.0254261 0 0 0 1.0254261
2078 1.0254261 2.1853284 0 0 1 1.0254261
2079 0.0695476 2.0695476 0 1 1 0.0695476
2080 0.0166545 1.0437455 0 0 0 1.0437455
2080 1.0437455 2.0166545 0 0 1 1.0437455
2081 0.2050548 2.2050548 0 1 1 0.2050548
2082 0.0482769 2.0482769 0 1 1 0.0482769
2083 0.0907289 1.0230041 0 0 0 1.0230041
2083 1.0230041 2.0907289 0 0 1 1.0230041
2084 0.1487180 1.0766435 0 0 0 1.0766435
2084 1.0766435 2.1487180 0 0 1 1.0766435
2085 0.0209194 2.0209194 0 1 1 0.0209194
2086 0.1509072 2.1509072 0 1 1 0.1509072
2087 0.0379711 1.0518250 0 0 0 1.0518250
2087 1.0518250 2.0379711 0 0 1 1.0518250
2088 0.0917423 1.0154639 0 0 0 1.0154639
2088 1.0154639 2.0917423 0 0 1 1.0154639
2089 0.0240686 2.0240686 0 1 1 0.0240686
2090 0.0416839 1.0432585 0 0 0 1.0432585
2090 1.0432585 2.0416839 0 0 1 1.0432585
2091 0.1872179 2.1872179 0 1 1 0.1872179
2092 0.0153073 2.0153073 0 1 1 0.0153073
2093 0.0246919 2.0246919 0 1 1 0.0246919
2094 0.1324086 2.1324086 0 1 1 0.1324086
2095 0.0455892 1.0569511 0 0 0 1.0569511
2095 1.0569511 2.0455892 0 0 1 1.0569511
2096 0.0738279 1.0332897 0 0 0 1.0332897
2096 1.0332897 2.0738279 0 0 1 1.0332897
2097 0.1416679 2.1416679 0 1 1 0.1416679
2098 0.0453549 1.0128415 0 0 0 1.0128415
2098 1.0128415 2.0453549 0 0 1 1.0128415
2099 0.1159232 2.1159232 0 1 1 0.1159232
2100 0.0368232 2.0368232 0 1 1 0.0368232
2101 0.2016412 2.2016412 0 1 1 0.2016412
2102 0.1334908 2.1334908 0 1 1 0.1334908
2103 0.2008577 1.0052594 0 0 0 1.0052594
2103 1.0052594 2.2008577 0 0 1 1.0052594
2104 0.2067548 2.2067548 0 1 1 0.2067548
2105 0.1878846 1.0019268 0 0 0 1.0019268
2105 1.0019268 2.1878846 0 0 1 1.0019268
2106 0.1118017 1.0707961 0 0 0 1.0707961
2106 1.0707961 2.1118017 0 0 1 1.0707961
2107 0.1405212 1.0153503 0 0 0 1.0153503
2107 1.0153503 2.1405212 0 0 1 1.0153503
2108 0.2219239 2.2219239 0 1 1 0.2219239
2109 0.0163628 1.0178086 0 0 0 1.0178086
2109 1.0178086 2.0163628 0 0 1 1.0178086
2110 0.0884721 2.0884721 0 1 1 0.0884721
2111 0.0535829 2.0535829 0 1 1 0.0535829
2112 0.0776893 2.0776893 0 1 1 0.0776893
2113 0.1575989 2.1575989 0 1 1 0.1575989
2114 0.1026082 2.1026082 0 1 1 0.1026082
2115 0.0708356 1.0189685 0 0 0 1.0189685
2115 1.0189685 2.0708356 0 0 1 1.0189685
2116 0.1062105 1.0575665 0 0 0 1.0575665
2116 1.0575665 2.1062105 0 0 1 1.0575665
2117 0.0363223 1.0315251 0 0 0 1.0315251
2117 1.0315251 2.0363223 0 0 1 1.0315251
2118 0.0757822 1.0278631 0 0 0 1.0278631
2118 1.0278631 2.0757822 0 0 1 1.0278631
2119 0.1487187 1.0394245 0 0 0 1.0394245
2119 1.0394245 2.1487187 0 0 1 1.0394245
2120 0.0438698 2.0438698 0 1 1 0.0438698
2121 0.1931238 2.1931238 0 1 1 0.1931238
2122 0.0792685 1.0405810 0 0 0 1.0405810
2122 1.0405810 2.0792685 0 0 1 1.0405810
2123 0.2239611 1.0252398 0 0 0 1.0252398
2123 1.0252398 2.2239611 0 0 1 1.0252398
2124 0.1023480 1.0717257 0 0 0 1.0717257
2124 1.0717257 2.1023480 0 0 1 1.0717257
2125 0.0002727 2.0002727 0 1 1 0.0002727
2126 0.1370968 2.1370968 0 1 1 0.1370968
2127 0.1676351 1.0571863 0 0 0 1.0571863
2127 1.0571863 2.1676351 0 0 1 1.0571863
2128 0.0109374 2.0109374 0 1 1 0.0109374
2129 0.0322601 2.0322601 0 1 1 0.0322601
2130 0.1979510 2.1979510 0 1 1 0.1979510
2131 0.0620541 1.0613408 0 0 0 1.0613408
2131 1.0613408 2.0620541 0 0 1 1.0613408
2132 0.1539224 1.0634333 0 0 0 1.0634333
2132 1.0634333 2.1539224 0 0 1 1.0634333
2133 0.1226144 2.1226144 0 1 1 0.1226144
2134 0.0332781 2.0332781 0 1 1 0.0332781
2135 0.0723751 2.0723751 0 1 1 0.0723751
2136 0.0561671 2.0561671 0 1 1 0.0561671
2137 0.0935577 2.0935577 0 1 1 0.0935577
2138 0.0504087 2.0504087 0 1 1 0.0504087
2139 0.1416885 2.1416885 0 1 1 0.1416885
2140 0.0711785 2.0711785 0 1 1 0.0711785
2141 0.2134758 2.2134758 0 1 1 0.2134758
2142 0.0521038 1.0672280 0 0 0 1.0672280
2142 1.0672280 2.0521038 0 0 1 1.0672280
2143 0.1319206 2.1319206 0 1 1 0.1319206
2144 0.0395273 1.0205161 0 0 0 1.0205161
2144 1.0205161 2.0395273 0 0 1 1.0205161
2145 0.1618908 1.0628300 0 0 0 1.0628300
2145 1.0628300 2.1618908 0 0 1 1.0628300
2146 0.1865050 2.1865050 0 1 1 0.1865050
2147 0.1504251 1.0722714 0 0 0 1.0722714
2147 1.0722714 2.1504251 0 0 1 1.0722714
2148 0.1656042 2.1656042 0 1 1 0.1656042
2149 0.0948031 2.0948031 0 1 1 0.0948031
2150 0.1378662 2.1378662 0 1 1 0.1378662
2151 0.1563124 1.0080033 0 0 0 1.0080033
2151 1.0080033 2.1563124 0 0 1 1.0080033
2152 0.2184481 1.0212778 0 0 0 1.0212778
2152 1.0212778 2.2184481 0 0 1 1.0212778
2153 0.0609114 1.0104671 0 0 0 1.0104671
2153 1.0104671 2.0609114 0 0 1 1.0104671
2154 0.0799916 2.0799916 0 1 1 0.0799916
2155 0.1167857 2.1167857 0 1 1 0.1167857
2156 0.0810782 2.0810782 0 1 1 0.0810782
2157 0.2197364 2.2197364 0 1 1 0.2197364
2158 0.1076497 2.1076497 0 1 1 0.1076497
2159 0.0760011 1.0491108 0 0 0 1.0491108
2159 1.0491108 2.0760011 0 0 1 1.0491108
2160 0.2188354 1.0054408 0 0 0 1.0054408
2160 1.0054408 2.2188354 0 0 1 1.0054408
2161 0.0332905 1.0747810 0 0 0 1.0747810
2161 1.0747810 2.0332905 0 0 1 1.0747810
2162 0.1319009 1.0205753 0 0 0 1.0205753
2162 1.0205753 2.1319009 0 0 1 1.0205753
2163 0.1430981 2.1430981 0 1 1 0.1430981
2164 0.1641689 2.1641689 0 1 1 0.1641689
2165 0.0677449 1.0340662 0 0 0 1.0340662
2165 1.0340662 2.0677449 0 0 1 1.0340662
2166 0.0240991 1.0544667 0 0 0 1.0544667
2166 1.0544667 2.0240991 0 0 1 1.0544667
2167 0.0229579 1.0375028 0 0 0 1.0375028
2167 1.0375028 2.0229579 0 0 1 1.0375028
2168 0.1808777 2.1808777 0 1 1 0.1808777
2169 0.1262088 1.0238343 0 0 0 1.0238343
2169 1.0238343 2.1262088 0 0 1 1.0238343
2170 0.0438485 2.0438485 0 1 1 0.0438485
2171 0.1046650 1.0317442 0 0 0 1.0317442
2171 1.0317442 2.1046650 0 0 1 1.0317442
2172 0.1617771 2.1617771 0 1 1 0.1617771
2173 0.2139813 2.2139813 0 1 1 0.2139813
2174 0.0720681 1.0700917 0 0 0 1.0700917
2174 1.0700917 2.0720681 0 0 1 1.0700917
2175 0.0053620 2.0053620 0 1 1 0.0053620
2176 0.0745563 2.0745563 0 1 1 0.0745563
2177 0.2217603 1.0006010 0 0 0 1.0006010
2177 1.0006010 2.2217603 0 0 1 1.0006010
2178 0.0931248 2.0931248 0 1 1 0.0931248
2179 0.1921255 1.0552891 0 0 0 1.0552891
2179 1.0552891 2.1921255 0 0 1 1.0552891
2180 0.1304443 2.1304443 0 1 1 0.1304443
2181 0.0597777 1.0030512 0 0 0 1.0030512
2181 1.0030512 2.0597777 0 0 1 1.0030512
2182 0.1345745 1.0204932 0 0 0 1.0204932
2182 1.0204932 2.1345745 0 0 1 1.0204932
2183 0.0098203 1.0519795 0 0 0 1.0519795
2183 1.0519795 2.0098203 0 0 1 1.0519795
2184 0.1186507 2.1186507 0 1 1 0.1186507
2185 0.1805024 2.1805024 0 1 1 0.1805024
2186 0.0311464 2.0311464 0 1 1 0.0311464
2187 0.1316181 1.0157307 0 0 0 1.0157307
2187 1.0157307 2.1316181 0 0 1 1.0157307
2188 0.0867519 1.0317410 0 0 0 1.0317410
2188 1.0317410 2.0867519 0 0 1 1.0317410
2189 0.0877549 2.0877549 0 1 1 0.0877549
2190 0.0555688 2.0555688 0 1 1 0.0555688
2191 0.0005972 1.0051834 0 0 0 1.0051834
2191 1.0051834 2.0005972 0 0 1 1.0051834
2192 0.0975089 2.0975089 0 1 1 0.0975089
2193 0.1581810 1.0080425 0 0 0 1.0080425
2193 1.0080425 2.1581810 0 0 1 1.0080425
2194 0.0143915 2.0143915 0 1 1 0.0143915
2195 0.1616404 1.0217520 0 0 0 1.0217520
2195 1.0217520 2.1616404 0 0 1 1.0217520
2196 0.1277770 1.0252687 0 0 0 1.0252687
2196 1.0252687 2.1277770 0 0 1 1.0252687
2197 0.0099567 1.0427062 0 0 0 1.0427062
2197 1.0427062 2.0099567 0 0 1 1.0427062
2198 0.0166146 1.0538032 0 0 0 1.0538032
2198 1.0538032 2.0166146 0 0 1 1.0538032
2199 0.1419489 1.0689977 0 0 0 1.0689977
2199 1.0689977 2.1419489 0 0 1 1.0689977
2200 0.0847208 2.0847208 0 1 1 0.0847208
2201 0.2228764 2.2228764 0 1 1 0.2228764
2202 0.1378346 2.1378346 0 1 1 0.1378346
2203 0.1971241 1.0737799 0 0 0 1.0737799
2203 1.0737799 2.1971241 0 0 1 1.0737799
2204 0.1541521 2.1541521 0 1 1 0.1541521
2205 0.0304932 2.0304932 0 1 1 0.0304932
2206 0.1263571 1.0201219 0 0 0 1.0201219
2206 1.0201219 2.1263571 0 0 1 1.0201219
2207 0.1027355 2.1027355 0 1 1 0.1027355
2208 0.1280726 1.0142648 0 0 0 1.0142648
2208 1.0142648 2.1280726 0 0 1 1.0142648
2209 0.0517562 1.0002015 0 0 0 1.0002015
2209 1.0002015 2.0517562 0 0 1 1.0002015
2210 0.1018164 2.1018164 0 1 1 0.1018164
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19564 0.1842562 2.1842562 0 1 1 0.1842562
19565 0.1768171 1.0730778 0 0 0 1.0730778
19565 1.0730778 2.1768171 0 0 1 1.0730778
19566 0.0622234 1.0058353 0 0 0 1.0058353
19566 1.0058353 2.0622234 0 0 1 1.0058353
19567 0.1474391 1.0351831 0 0 0 1.0351831
19567 1.0351831 2.1474391 0 0 1 1.0351831
19568 0.1058688 1.0580476 0 0 0 1.0580476
19568 1.0580476 2.1058688 0 0 1 1.0580476
19569 0.1764490 2.1764490 0 1 1 0.1764490
19570 0.0698111 1.0632325 0 0 0 1.0632325
19570 1.0632325 2.0698111 0 0 1 1.0632325
19571 0.1762437 2.1762437 0 1 1 0.1762437
19572 0.0916049 1.0647027 0 0 0 1.0647027
19572 1.0647027 2.0916049 0 0 1 1.0647027
19573 0.0958148 2.0958148 0 1 1 0.0958148
19574 0.0374370 2.0374370 0 1 1 0.0374370
19575 0.0154240 1.0652735 0 0 0 1.0652735
19575 1.0652735 2.0154240 0 0 1 1.0652735
19576 0.1464185 2.1464185 0 1 1 0.1464185
19577 0.2084632 1.0327865 0 0 0 1.0327865
19577 1.0327865 2.2084632 0 0 1 1.0327865
19578 0.1366583 2.1366583 0 1 1 0.1366583
19579 0.0154121 1.0062723 0 0 0 1.0062723
19579 1.0062723 2.0154121 0 0 1 1.0062723
19580 0.0541255 1.0429602 0 0 0 1.0429602
19580 1.0429602 2.0541255 0 0 1 1.0429602
19581 0.2192688 2.2192688 0 1 1 0.2192688
19582 0.1297648 2.1297648 0 1 1 0.1297648
19583 0.0977000 2.0977000 0 1 1 0.0977000
19584 0.1244804 1.0716375 0 0 0 1.0716375
19584 1.0716375 2.1244804 0 0 1 1.0716375
19585 0.1237880 1.0060994 0 0 0 1.0060994
19585 1.0060994 2.1237880 0 0 1 1.0060994
19586 0.1155623 2.1155623 0 1 1 0.1155623
19587 0.0951240 1.0548922 0 0 0 1.0548922
19587 1.0548922 2.0951240 0 0 1 1.0548922
19588 0.0252126 2.0252126 0 1 1 0.0252126
19589 0.1173548 2.1173548 0 1 1 0.1173548
19590 0.0040168 1.0237909 0 0 0 1.0237909
19590 1.0237909 2.0040168 0 0 1 1.0237909
19591 0.2055351 2.2055351 0 1 1 0.2055351
19592 0.0746107 1.0366855 0 0 0 1.0366855
19592 1.0366855 2.0746107 0 0 1 1.0366855
19593 0.1287624 2.1287624 0 1 1 0.1287624
19594 0.2123188 1.0067797 0 0 0 1.0067797
19594 1.0067797 2.2123188 0 0 1 1.0067797
19595 0.2215071 1.0152120 0 0 0 1.0152120
19595 1.0152120 2.2215071 0 0 1 1.0152120
19596 0.0778775 2.0778775 0 1 1 0.0778775
19597 0.1862393 1.0516505 0 0 0 1.0516505
19597 1.0516505 2.1862393 0 0 1 1.0516505
19598 0.0602405 1.0555186 0 0 0 1.0555186
19598 1.0555186 2.0602405 0 0 1 1.0555186
19599 0.2277167 1.0162376 0 0 0 1.0162376
19599 1.0162376 2.2277167 0 0 1 1.0162376
19600 0.1020320 2.1020320 0 1 1 0.1020320
19601 0.1710823 1.0723878 0 0 0 1.0723878
19601 1.0723878 2.1710823 0 0 1 1.0723878
19602 0.0534522 1.0250775 0 0 0 1.0250775
19602 1.0250775 2.0534522 0 0 1 1.0250775
19603 0.1091708 2.1091708 0 1 1 0.1091708
19604 0.1204383 2.1204383 0 1 1 0.1204383
19605 0.1472593 1.0423131 0 0 0 1.0423131
19605 1.0423131 2.1472593 0 0 1 1.0423131
19606 0.2162310 2.2162310 0 1 1 0.2162310
19607 0.1496709 1.0579026 0 0 0 1.0579026
19607 1.0579026 2.1496709 0 0 1 1.0579026
19608 0.0879145 2.0879145 0 1 1 0.0879145
19609 0.1353964 1.0256584 0 0 0 1.0256584
19609 1.0256584 2.1353964 0 0 1 1.0256584
19610 0.1431404 1.0263358 0 0 0 1.0263358
19610 1.0263358 2.1431404 0 0 1 1.0263358
19611 0.0415751 2.0415751 0 1 1 0.0415751
19612 0.0554070 1.0066703 0 0 0 1.0066703
19612 1.0066703 2.0554070 0 0 1 1.0066703
19613 0.0661886 2.0661886 0 1 1 0.0661886
19614 0.1014322 1.0376900 0 0 0 1.0376900
19614 1.0376900 2.1014322 0 0 1 1.0376900
19615 0.0944678 2.0944678 0 1 1 0.0944678
19616 0.0826912 1.0629825 0 0 0 1.0629825
19616 1.0629825 2.0826912 0 0 1 1.0629825
19617 0.2188982 1.0747194 0 0 0 1.0747194
19617 1.0747194 2.2188982 0 0 1 1.0747194
19618 0.1977688 1.0189592 0 0 0 1.0189592
19618 1.0189592 2.1977688 0 0 1 1.0189592
19619 0.0566979 1.0671520 0 0 0 1.0671520
19619 1.0671520 2.0566979 0 0 1 1.0671520
19620 0.0673853 2.0673853 0 1 1 0.0673853
19621 0.2021122 2.2021122 0 1 1 0.2021122
19622 0.1253561 1.0109510 0 0 0 1.0109510
19622 1.0109510 2.1253561 0 0 1 1.0109510
19623 0.2300604 1.0395216 0 0 0 1.0395216
19623 1.0395216 2.2300604 0 0 1 1.0395216
19624 0.1073729 2.1073729 0 1 1 0.1073729
19625 0.1186672 2.1186672 0 1 1 0.1186672
19626 0.0424281 2.0424281 0 1 1 0.0424281
19627 0.2091997 1.0507389 0 0 0 1.0507389
19627 1.0507389 2.2091997 0 0 1 1.0507389
19628 0.0427964 1.0554102 0 0 0 1.0554102
19628 1.0554102 2.0427964 0 0 1 1.0554102
19629 0.1162651 1.0307720 0 0 0 1.0307720
19629 1.0307720 2.1162651 0 0 1 1.0307720
19630 0.0025477 1.0767990 0 0 0 1.0767990
19630 1.0767990 2.0025477 0 0 1 1.0767990
19631 0.0370971 1.0017072 0 0 0 1.0017072
19631 1.0017072 2.0370971 0 0 1 1.0017072
19632 0.1186691 1.0384012 0 0 0 1.0384012
19632 1.0384012 2.1186691 0 0 1 1.0384012
19633 0.0971675 1.0071975 0 0 0 1.0071975
19633 1.0071975 2.0971675 0 0 1 1.0071975
19634 0.0586147 1.0156614 0 0 0 1.0156614
19634 1.0156614 2.0586147 0 0 1 1.0156614
19635 0.1464423 2.1464423 0 1 1 0.1464423
19636 0.0362519 1.0125924 0 0 0 1.0125924
19636 1.0125924 2.0362519 0 0 1 1.0125924
19637 0.0522208 2.0522208 0 1 1 0.0522208
19638 0.1657864 1.0238568 0 0 0 1.0238568
19638 1.0238568 2.1657864 0 0 1 1.0238568
19639 0.2109776 1.0335861 0 0 0 1.0335861
19639 1.0335861 2.2109776 0 0 1 1.0335861
19640 0.1801406 2.1801406 0 1 1 0.1801406
19641 0.0861362 1.0415574 0 0 0 1.0415574
19641 1.0415574 2.0861362 0 0 1 1.0415574
19642 0.1856362 1.0736636 0 0 0 1.0736636
19642 1.0736636 2.1856362 0 0 1 1.0736636
19643 0.1707637 1.0141153 0 0 0 1.0141153
19643 1.0141153 2.1707637 0 0 1 1.0141153
19644 0.2195616 2.2195616 0 1 1 0.2195616
19645 0.1884248 1.0429862 0 0 0 1.0429862
19645 1.0429862 2.1884248 0 0 1 1.0429862
19646 0.0564704 2.0564704 0 1 1 0.0564704
19647 0.0625018 1.0034512 0 0 0 1.0034512
19647 1.0034512 2.0625018 0 0 1 1.0034512
19648 0.0139863 2.0139863 0 1 1 0.0139863
19649 0.1770540 1.0531500 0 0 0 1.0531500
19649 1.0531500 2.1770540 0 0 1 1.0531500
19650 0.0826399 2.0826399 0 1 1 0.0826399
19651 0.0506694 2.0506694 0 1 1 0.0506694
19652 0.0823742 2.0823742 0 1 1 0.0823742
19653 0.2009946 2.2009946 0 1 1 0.2009946
19654 0.1586300 2.1586300 0 1 1 0.1586300
19655 0.2289629 1.0598427 0 0 0 1.0598427
19655 1.0598427 2.2289629 0 0 1 1.0598427
19656 0.1656025 1.0667262 0 0 0 1.0667262
19656 1.0667262 2.1656025 0 0 1 1.0667262
19657 0.1352048 1.0355863 0 0 0 1.0355863
19657 1.0355863 2.1352048 0 0 1 1.0355863
19658 0.1162632 1.0648765 0 0 0 1.0648765
19658 1.0648765 2.1162632 0 0 1 1.0648765
19659 0.1523718 1.0295501 0 0 0 1.0295501
19659 1.0295501 2.1523718 0 0 1 1.0295501
19660 0.0851702 1.0532641 0 0 0 1.0532641
19660 1.0532641 2.0851702 0 0 1 1.0532641
19661 0.0066923 1.0718218 0 0 0 1.0718218
19661 1.0718218 2.0066923 0 0 1 1.0718218
19662 0.1250753 1.0160962 0 0 0 1.0160962
19662 1.0160962 2.1250753 0 0 1 1.0160962
19663 0.2121915 1.0671300 0 0 0 1.0671300
19663 1.0671300 2.2121915 0 0 1 1.0671300
19664 0.2103690 2.2103690 0 1 1 0.2103690
19665 0.0147405 2.0147405 0 1 1 0.0147405
19666 0.1592109 1.0033887 0 0 0 1.0033887
19666 1.0033887 2.1592109 0 0 1 1.0033887
19667 0.1081410 1.0479136 0 0 0 1.0479136
19667 1.0479136 2.1081410 0 0 1 1.0479136
19668 0.0260371 2.0260371 0 1 1 0.0260371
19669 0.1319408 2.1319408 0 1 1 0.1319408
19670 0.1185319 2.1185319 0 1 1 0.1185319
19671 0.0963377 1.0462563 0 0 0 1.0462563
19671 1.0462563 2.0963377 0 0 1 1.0462563
19672 0.0450126 2.0450126 0 1 1 0.0450126
19673 0.1377959 1.0122990 0 0 0 1.0122990
19673 1.0122990 2.1377959 0 0 1 1.0122990
19674 0.2156127 1.0498856 0 0 0 1.0498856
19674 1.0498856 2.2156127 0 0 1 1.0498856
19675 0.1094310 2.1094310 0 1 1 0.1094310
19676 0.0346039 2.0346039 0 1 1 0.0346039
19677 0.0390792 1.0606602 0 0 0 1.0606602
19677 1.0606602 2.0390792 0 0 1 1.0606602
19678 0.2176685 2.2176685 0 1 1 0.2176685
19679 0.1691041 1.0487816 0 0 0 1.0487816
19679 1.0487816 2.1691041 0 0 1 1.0487816
19680 0.1403194 2.1403194 0 1 1 0.1403194
19681 0.1465885 1.0620979 0 0 0 1.0620979
19681 1.0620979 2.1465885 0 0 1 1.0620979
19682 0.1281269 1.0106859 0 0 0 1.0106859
19682 1.0106859 2.1281269 0 0 1 1.0106859
19683 0.2294420 2.2294420 0 1 1 0.2294420
19684 0.0954412 1.0041303 0 0 0 1.0041303
19684 1.0041303 2.0954412 0 0 1 1.0041303
19685 0.0420537 1.0350690 0 0 0 1.0350690
19685 1.0350690 2.0420537 0 0 1 1.0350690
19686 0.0216293 2.0216293 0 1 1 0.0216293
19687 0.1384714 1.0633130 0 0 0 1.0633130
19687 1.0633130 2.1384714 0 0 1 1.0633130
19688 0.0923201 2.0923201 0 1 1 0.0923201
19689 0.1098429 1.0600475 0 0 0 1.0600475
19689 1.0600475 2.1098429 0 0 1 1.0600475
19690 0.0283337 1.0460576 0 0 0 1.0460576
19690 1.0460576 2.0283337 0 0 1 1.0460576
19691 0.1422750 1.0708690 0 0 0 1.0708690
19691 1.0708690 2.1422750 0 0 1 1.0708690
19692 0.1718500 2.1718500 0 1 1 0.1718500
19693 0.0450940 1.0129201 0 0 0 1.0129201
19693 1.0129201 2.0450940 0 0 1 1.0129201
19694 0.0722091 2.0722091 0 1 1 0.0722091
19695 0.2057977 2.2057977 0 1 1 0.2057977
19696 0.0598456 1.0075036 0 0 0 1.0075036
19696 1.0075036 2.0598456 0 0 1 1.0075036
19697 0.1641648 2.1641648 0 1 1 0.1641648
19698 0.1507367 1.0769063 0 0 0 1.0769063
19698 1.0769063 2.1507367 0 0 1 1.0769063
19699 0.0810161 2.0810161 0 1 1 0.0810161
19700 0.1006789 2.1006789 0 1 1 0.1006789
19701 0.1765933 2.1765933 0 1 1 0.1765933
19702 0.0052428 2.0052428 0 1 1 0.0052428
19703 0.1113149 1.0505214 0 0 0 1.0505214
19703 1.0505214 2.1113149 0 0 1 1.0505214
19704 0.0201222 2.0201222 0 1 1 0.0201222
19705 0.0535596 2.0535596 0 1 1 0.0535596
19706 0.0724402 2.0724402 0 1 1 0.0724402
19707 0.1458366 2.1458366 0 1 1 0.1458366
19708 0.1212090 1.0059296 0 0 0 1.0059296
19708 1.0059296 2.1212090 0 0 1 1.0059296
19709 0.1607282 2.1607282 0 1 1 0.1607282
19710 0.0989086 1.0521521 0 0 0 1.0521521
19710 1.0521521 2.0989086 0 0 1 1.0521521
19711 0.1402453 2.1402453 0 1 1 0.1402453
19712 0.0515876 2.0515876 0 1 1 0.0515876
19713 0.1640625 2.1640625 0 1 1 0.1640625
19714 0.1890070 2.1890070 0 1 1 0.1890070
19715 0.0552985 1.0426507 0 0 0 1.0426507
19715 1.0426507 2.0552985 0 0 1 1.0426507
19716 0.0249633 2.0249633 0 1 1 0.0249633
19717 0.1572249 2.1572249 0 1 1 0.1572249
19718 0.0334089 1.0633441 0 0 0 1.0633441
19718 1.0633441 2.0334089 0 0 1 1.0633441
19719 0.2215925 2.2215925 0 1 1 0.2215925
19720 0.0482572 2.0482572 0 1 1 0.0482572
19721 0.1593822 1.0597064 0 0 0 1.0597064
19721 1.0597064 2.1593822 0 0 1 1.0597064
19722 0.0565007 2.0565007 0 1 1 0.0565007
19723 0.1541664 2.1541664 0 1 1 0.1541664
19724 0.0650368 2.0650368 0 1 1 0.0650368
19725 0.0815730 2.0815730 0 1 1 0.0815730
19726 0.1216073 2.1216073 0 1 1 0.1216073
19727 0.1162081 1.0046952 0 0 0 1.0046952
19727 1.0046952 2.1162081 0 0 1 1.0046952
19728 0.0352179 1.0614700 0 0 0 1.0614700
19728 1.0614700 2.0352179 0 0 1 1.0614700
19729 0.1891970 2.1891970 0 1 1 0.1891970
19730 0.0784933 2.0784933 0 1 1 0.0784933
19731 0.0410567 2.0410567 0 1 1 0.0410567
19732 0.1960601 2.1960601 0 1 1 0.1960601
19733 0.1382952 1.0500276 0 0 0 1.0500276
19733 1.0500276 2.1382952 0 0 1 1.0500276
19734 0.1004892 1.0069714 0 0 0 1.0069714
19734 1.0069714 2.1004892 0 0 1 1.0069714
19735 0.1953849 1.0755818 0 0 0 1.0755818
19735 1.0755818 2.1953849 0 0 1 1.0755818
19736 0.1835047 1.0088183 0 0 0 1.0088183
19736 1.0088183 2.1835047 0 0 1 1.0088183
19737 0.1878680 1.0623600 0 0 0 1.0623600
19737 1.0623600 2.1878680 0 0 1 1.0623600
19738 0.1171297 2.1171297 0 1 1 0.1171297
19739 0.1728198 2.1728198 0 1 1 0.1728198
19740 0.2033075 2.2033075 0 1 1 0.2033075
19741 0.0389152 2.0389152 0 1 1 0.0389152
19742 0.0727964 1.0635907 0 0 0 1.0635907
19742 1.0635907 2.0727964 0 0 1 1.0635907
19743 0.1747334 2.1747334 0 1 1 0.1747334
19744 0.0825347 2.0825347 0 1 1 0.0825347
19745 0.0194081 2.0194081 0 1 1 0.0194081
19746 0.0548473 1.0190517 0 0 0 1.0190517
19746 1.0190517 2.0548473 0 0 1 1.0190517
19747 0.0455689 1.0147189 0 0 0 1.0147189
19747 1.0147189 2.0455689 0 0 1 1.0147189
19748 0.1561084 2.1561084 0 1 1 0.1561084
19749 0.0770342 2.0770342 0 1 1 0.0770342
19750 0.0637507 2.0637507 0 1 1 0.0637507
19751 0.0284542 1.0205617 0 0 0 1.0205617
19751 1.0205617 2.0284542 0 0 1 1.0205617
19752 0.2087819 1.0295894 0 0 0 1.0295894
19752 1.0295894 2.2087819 0 0 1 1.0295894
19753 0.1479606 1.0209514 0 0 0 1.0209514
19753 1.0209514 2.1479606 0 0 1 1.0209514
19754 0.2005178 2.2005178 0 1 1 0.2005178
19755 0.0757570 1.0164945 0 0 0 1.0164945
19755 1.0164945 2.0757570 0 0 1 1.0164945
19756 0.0710796 2.0710796 0 1 1 0.0710796
19757 0.1865004 1.0677054 0 0 0 1.0677054
19757 1.0677054 2.1865004 0 0 1 1.0677054
19758 0.0402392 2.0402392 0 1 1 0.0402392
19759 0.0846511 1.0155599 0 0 0 1.0155599
19759 1.0155599 2.0846511 0 0 1 1.0155599
19760 0.1360862 2.1360862 0 1 1 0.1360862
19761 0.0938588 1.0584766 0 0 0 1.0584766
19761 1.0584766 2.0938588 0 0 1 1.0584766
19762 0.0948574 2.0948574 0 1 1 0.0948574
19763 0.1701745 2.1701745 0 1 1 0.1701745
19764 0.1679869 2.1679869 0 1 1 0.1679869
19765 0.1386420 1.0369771 0 0 0 1.0369771
19765 1.0369771 2.1386420 0 0 1 1.0369771
19766 0.1347741 2.1347741 0 1 1 0.1347741
19767 0.1741691 2.1741691 0 1 1 0.1741691
19768 0.1619471 2.1619471 0 1 1 0.1619471
19769 0.0400402 1.0277399 0 0 0 1.0277399
19769 1.0277399 2.0400402 0 0 1 1.0277399
19770 0.0994476 2.0994476 0 1 1 0.0994476
19771 0.0213224 1.0239598 0 0 0 1.0239598
19771 1.0239598 2.0213224 0 0 1 1.0239598
19772 0.0275460 1.0161804 0 0 0 1.0161804
19772 1.0161804 2.0275460 0 0 1 1.0161804
19773 0.2251610 1.0540834 0 0 0 1.0540834
19773 1.0540834 2.2251610 0 0 1 1.0540834
19774 0.0609467 1.0096167 0 0 0 1.0096167
19774 1.0096167 2.0609467 0 0 1 1.0096167
19775 0.1480618 1.0676243 0 0 0 1.0676243
19775 1.0676243 2.1480618 0 0 1 1.0676243
19776 0.0439319 1.0764257 0 0 0 1.0764257
19776 1.0764257 2.0439319 0 0 1 1.0764257
19777 0.1699309 2.1699309 0 1 1 0.1699309
19778 0.0991849 2.0991849 0 1 1 0.0991849
19779 0.0270074 1.0766893 0 0 0 1.0766893
19779 1.0766893 2.0270074 0 0 1 1.0766893
19780 0.2138983 2.2138983 0 1 1 0.2138983
19781 0.1650950 1.0425328 0 0 0 1.0425328
19781 1.0425328 2.1650950 0 0 1 1.0425328
19782 0.1724940 2.1724940 0 1 1 0.1724940
19783 0.0451919 2.0451919 0 1 1 0.0451919
19784 0.1008851 1.0301154 0 0 0 1.0301154
19784 1.0301154 2.1008851 0 0 1 1.0301154
19785 0.0835708 2.0835708 0 1 1 0.0835708
19786 0.0106811 2.0106811 0 1 1 0.0106811
19787 0.1058326 2.1058326 0 1 1 0.1058326
19788 0.1917269 2.1917269 0 1 1 0.1917269
19789 0.1309879 2.1309879 0 1 1 0.1309879
19790 0.0091904 1.0366950 0 0 0 1.0366950
19790 1.0366950 2.0091904 0 0 1 1.0366950
19791 0.1223211 1.0430030 0 0 0 1.0430030
19791 1.0430030 2.1223211 0 0 1 1.0430030
19792 0.1233015 2.1233015 0 1 1 0.1233015
19793 0.0327029 2.0327029 0 1 1 0.0327029
19794 0.0114389 1.0697619 0 0 0 1.0697619
19794 1.0697619 2.0114389 0 0 1 1.0697619
19795 0.1419620 1.0003505 0 0 0 1.0003505
19795 1.0003505 2.1419620 0 0 1 1.0003505
19796 0.0915956 1.0131540 0 0 0 1.0131540
19796 1.0131540 2.0915956 0 0 1 1.0131540
19797 0.0498378 1.0595975 0 0 0 1.0595975
19797 1.0595975 2.0498378 0 0 1 1.0595975
19798 0.0077115 1.0641804 0 0 0 1.0641804
19798 1.0641804 2.0077115 0 0 1 1.0641804
19799 0.0151519 1.0512847 0 0 0 1.0512847
19799 1.0512847 2.0151519 0 0 1 1.0512847
19800 0.0859732 2.0859732 0 1 1 0.0859732
19801 0.1218878 1.0309144 0 0 0 1.0309144
19801 1.0309144 2.1218878 0 0 1 1.0309144
19802 0.0918643 1.0071848 0 0 0 1.0071848
19802 1.0071848 2.0918643 0 0 1 1.0071848
19803 0.1429872 1.0684495 0 0 0 1.0684495
19803 1.0684495 2.1429872 0 0 1 1.0684495
19804 0.0389877 1.0029560 0 0 0 1.0029560
19804 1.0029560 2.0389877 0 0 1 1.0029560
19805 0.0580969 1.0281434 0 0 0 1.0281434
19805 1.0281434 2.0580969 0 0 1 1.0281434
19806 0.1178813 2.1178813 0 1 1 0.1178813
19807 0.0393115 1.0348068 0 0 0 1.0348068
19807 1.0348068 2.0393115 0 0 1 1.0348068
19808 0.2256299 1.0493300 0 0 0 1.0493300
19808 1.0493300 2.2256299 0 0 1 1.0493300
19809 0.0667993 2.0667993 0 1 1 0.0667993
19810 0.1947467 2.1947467 0 1 1 0.1947467
19811 0.1950243 2.1950243 0 1 1 0.1950243
19812 0.1926519 1.0089937 0 0 0 1.0089937
19812 1.0089937 2.1926519 0 0 1 1.0089937
19813 0.1828711 2.1828711 0 1 1 0.1828711
19814 0.1195748 1.0380348 0 0 0 1.0380348
19814 1.0380348 2.1195748 0 0 1 1.0380348
19815 0.0960787 2.0960787 0 1 1 0.0960787
19816 0.1115920 2.1115920 0 1 1 0.1115920
19817 0.0037174 2.0037174 0 1 1 0.0037174
19818 0.1179025 1.0650220 0 0 0 1.0650220
19818 1.0650220 2.1179025 0 0 1 1.0650220
19819 0.0824839 2.0824839 0 1 1 0.0824839
19820 0.1831217 1.0729814 0 0 0 1.0729814
19820 1.0729814 2.1831217 0 0 1 1.0729814
19821 0.2250110 2.2250110 0 1 1 0.2250110
19822 0.1541155 1.0269841 0 0 0 1.0269841
19822 1.0269841 2.1541155 0 0 1 1.0269841
19823 0.1920412 1.0254490 0 0 0 1.0254490
19823 1.0254490 2.1920412 0 0 1 1.0254490
19824 0.1418521 1.0369924 0 0 0 1.0369924
19824 1.0369924 2.1418521 0 0 1 1.0369924
19825 0.0399314 2.0399314 0 1 1 0.0399314
19826 0.2108946 2.2108946 0 1 1 0.2108946
19827 0.1373156 2.1373156 0 1 1 0.1373156
19828 0.1056416 1.0271752 0 0 0 1.0271752
19828 1.0271752 2.1056416 0 0 1 1.0271752
19829 0.1593831 1.0588354 0 0 0 1.0588354
19829 1.0588354 2.1593831 0 0 1 1.0588354
19830 0.0875801 2.0875801 0 1 1 0.0875801
19831 0.0948321 2.0948321 0 1 1 0.0948321
19832 0.1942199 2.1942199 0 1 1 0.1942199
19833 0.0197909 1.0567548 0 0 0 1.0567548
19833 1.0567548 2.0197909 0 0 1 1.0567548
19834 0.2078542 2.2078542 0 1 1 0.2078542
19835 0.1831436 1.0509058 0 0 0 1.0509058
19835 1.0509058 2.1831436 0 0 1 1.0509058
19836 0.0189856 2.0189856 0 1 1 0.0189856
19837 0.1455753 2.1455753 0 1 1 0.1455753
19838 0.0929305 1.0599297 0 0 0 1.0599297
19838 1.0599297 2.0929305 0 0 1 1.0599297
19839 0.0852918 2.0852918 0 1 1 0.0852918
19840 0.0348726 2.0348726 0 1 1 0.0348726
19841 0.0115281 2.0115281 0 1 1 0.0115281
19842 0.1442909 2.1442909 0 1 1 0.1442909
19843 0.0413794 2.0413794 0 1 1 0.0413794
19844 0.2013618 2.2013618 0 1 1 0.2013618
19845 0.1047980 1.0120763 0 0 0 1.0120763
19845 1.0120763 2.1047980 0 0 1 1.0120763
19846 0.1799723 2.1799723 0 1 1 0.1799723
19847 0.1270234 1.0527759 0 0 0 1.0527759
19847 1.0527759 2.1270234 0 0 1 1.0527759
19848 0.2060849 1.0132431 0 0 0 1.0132431
19848 1.0132431 2.2060849 0 0 1 1.0132431
19849 0.0165270 2.0165270 0 1 1 0.0165270
19850 0.1746113 2.1746113 0 1 1 0.1746113
19851 0.1267862 1.0525284 0 0 0 1.0525284
19851 1.0525284 2.1267862 0 0 1 1.0525284
19852 0.0414636 1.0371445 0 0 0 1.0371445
19852 1.0371445 2.0414636 0 0 1 1.0371445
19853 0.1119223 1.0396564 0 0 0 1.0396564
19853 1.0396564 2.1119223 0 0 1 1.0396564
19854 0.0877452 2.0877452 0 1 1 0.0877452
19855 0.1584890 2.1584890 0 1 1 0.1584890
19856 0.2113730 2.2113730 0 1 1 0.2113730
19857 0.0189864 2.0189864 0 1 1 0.0189864
19858 0.0691037 2.0691037 0 1 1 0.0691037
19859 0.1689359 2.1689359 0 1 1 0.1689359
19860 0.0404867 2.0404867 0 1 1 0.0404867
19861 0.0682212 2.0682212 0 1 1 0.0682212
19862 0.0587602 1.0495676 0 0 0 1.0495676
19862 1.0495676 2.0587602 0 0 1 1.0495676
19863 0.0518613 1.0517282 0 0 0 1.0517282
19863 1.0517282 2.0518613 0 0 1 1.0517282
19864 0.0203583 1.0481068 0 0 0 1.0481068
19864 1.0481068 2.0203583 0 0 1 1.0481068
19865 0.0308079 1.0507284 0 0 0 1.0507284
19865 1.0507284 2.0308079 0 0 1 1.0507284
19866 0.2225109 2.2225109 0 1 1 0.2225109
19867 0.1604079 1.0726334 0 0 0 1.0726334
19867 1.0726334 2.1604079 0 0 1 1.0726334
19868 0.1051536 2.1051536 0 1 1 0.1051536
19869 0.2163515 2.2163515 0 1 1 0.2163515
19870 0.1449575 1.0049498 0 0 0 1.0049498
19870 1.0049498 2.1449575 0 0 1 1.0049498
19871 0.1768518 2.1768518 0 1 1 0.1768518
19872 0.2038299 1.0406140 0 0 0 1.0406140
19872 1.0406140 2.2038299 0 0 1 1.0406140
19873 0.0580879 2.0580879 0 1 1 0.0580879
19874 0.0620018 1.0006907 0 0 0 1.0006907
19874 1.0006907 2.0620018 0 0 1 1.0006907
19875 0.0999824 1.0608555 0 0 0 1.0608555
19875 1.0608555 2.0999824 0 0 1 1.0608555
19876 0.1118834 1.0519232 0 0 0 1.0519232
19876 1.0519232 2.1118834 0 0 1 1.0519232
19877 0.2192606 2.2192606 0 1 1 0.2192606
19878 0.0138950 1.0678250 0 0 0 1.0678250
19878 1.0678250 2.0138950 0 0 1 1.0678250
19879 0.0749141 2.0749141 0 1 1 0.0749141
19880 0.1089122 1.0102584 0 0 0 1.0102584
19880 1.0102584 2.1089122 0 0 1 1.0102584
19881 0.1601131 2.1601131 0 1 1 0.1601131
19882 0.1154747 1.0218365 0 0 0 1.0218365
19882 1.0218365 2.1154747 0 0 1 1.0218365
19883 0.2157303 1.0064772 0 0 0 1.0064772
19883 1.0064772 2.2157303 0 0 1 1.0064772
19884 0.0019937 1.0024894 0 0 0 1.0024894
19884 1.0024894 2.0019937 0 0 1 1.0024894
19885 0.0906346 1.0361869 0 0 0 1.0361869
19885 1.0361869 2.0906346 0 0 1 1.0361869
19886 0.0646696 1.0340854 0 0 0 1.0340854
19886 1.0340854 2.0646696 0 0 1 1.0340854
19887 0.2053621 1.0432017 0 0 0 1.0432017
19887 1.0432017 2.2053621 0 0 1 1.0432017
19888 0.0652249 2.0652249 0 1 1 0.0652249
19889 0.0211545 1.0007123 0 0 0 1.0007123
19889 1.0007123 2.0211545 0 0 1 1.0007123
19890 0.2056787 2.2056787 0 1 1 0.2056787
19891 0.0541391 1.0544206 0 0 0 1.0544206
19891 1.0544206 2.0541391 0 0 1 1.0544206
19892 0.0886056 1.0231016 0 0 0 1.0231016
19892 1.0231016 2.0886056 0 0 1 1.0231016
19893 0.2146667 2.2146667 0 1 1 0.2146667
19894 0.2051709 2.2051709 0 1 1 0.2051709
19895 0.0348873 1.0415058 0 0 0 1.0415058
19895 1.0415058 2.0348873 0 0 1 1.0415058
19896 0.1303033 2.1303033 0 1 1 0.1303033
19897 0.1752447 1.0595668 0 0 0 1.0595668
19897 1.0595668 2.1752447 0 0 1 1.0595668
19898 0.1015977 1.0163026 0 0 0 1.0163026
19898 1.0163026 2.1015977 0 0 1 1.0163026
19899 0.1545476 1.0484688 0 0 0 1.0484688
19899 1.0484688 2.1545476 0 0 1 1.0484688
19900 0.2167056 2.2167056 0 1 1 0.2167056
19901 0.1325649 2.1325649 0 1 1 0.1325649
19902 0.1797057 2.1797057 0 1 1 0.1797057
19903 0.1834282 1.0059356 0 0 0 1.0059356
19903 1.0059356 2.1834282 0 0 1 1.0059356
19904 0.0356289 2.0356289 0 1 1 0.0356289
19905 0.0396142 2.0396142 0 1 1 0.0396142
19906 0.2137441 2.2137441 0 1 1 0.2137441
19907 0.2306483 2.2306483 0 1 1 0.2306483
19908 0.1945473 1.0268138 0 0 0 1.0268138
19908 1.0268138 2.1945473 0 0 1 1.0268138
19909 0.0361103 2.0361103 0 1 1 0.0361103
19910 0.0142813 1.0409865 0 0 0 1.0409865
19910 1.0409865 2.0142813 0 0 1 1.0409865
19911 0.1634177 1.0144782 0 0 0 1.0144782
19911 1.0144782 2.1634177 0 0 1 1.0144782
19912 0.2064379 1.0092060 0 0 0 1.0092060
19912 1.0092060 2.2064379 0 0 1 1.0092060
19913 0.1992414 2.1992414 0 1 1 0.1992414
19914 0.0712182 1.0237713 0 0 0 1.0237713
19914 1.0237713 2.0712182 0 0 1 1.0237713
19915 0.0111036 1.0536508 0 0 0 1.0536508
19915 1.0536508 2.0111036 0 0 1 1.0536508
19916 0.1251479 1.0134127 0 0 0 1.0134127
19916 1.0134127 2.1251479 0 0 1 1.0134127
19917 0.0438408 1.0142476 0 0 0 1.0142476
19917 1.0142476 2.0438408 0 0 1 1.0142476
19918 0.1597384 2.1597384 0 1 1 0.1597384
19919 0.1503948 1.0578327 0 0 0 1.0578327
19919 1.0578327 2.1503948 0 0 1 1.0578327
19920 0.0841759 2.0841759 0 1 1 0.0841759
19921 0.2225381 1.0254258 0 0 0 1.0254258
19921 1.0254258 2.2225381 0 0 1 1.0254258
19922 0.0454647 2.0454647 0 1 1 0.0454647
19923 0.1851504 2.1851504 0 1 1 0.1851504
19924 0.0678963 1.0684284 0 0 0 1.0684284
19924 1.0684284 2.0678963 0 0 1 1.0684284
19925 0.0976727 2.0976727 0 1 1 0.0976727
19926 0.1308051 1.0084084 0 0 0 1.0084084
19926 1.0084084 2.1308051 0 0 1 1.0084084
19927 0.2252584 2.2252584 0 1 1 0.2252584
19928 0.0728013 2.0728013 0 1 1 0.0728013
19929 0.0529904 2.0529904 0 1 1 0.0529904
19930 0.0812319 2.0812319 0 1 1 0.0812319
19931 0.0663578 2.0663578 0 1 1 0.0663578
19932 0.1575522 1.0530397 0 0 0 1.0530397
19932 1.0530397 2.1575522 0 0 1 1.0530397
19933 0.0798201 1.0577208 0 0 0 1.0577208
19933 1.0577208 2.0798201 0 0 1 1.0577208
19934 0.2009521 2.2009521 0 1 1 0.2009521
19935 0.0790162 1.0436769 0 0 0 1.0436769
19935 1.0436769 2.0790162 0 0 1 1.0436769
19936 0.2126911 2.2126911 0 1 1 0.2126911
19937 0.1219692 2.1219692 0 1 1 0.1219692
19938 0.0455087 1.0450992 0 0 0 1.0450992
19938 1.0450992 2.0455087 0 0 1 1.0450992
19939 0.0861460 1.0055803 0 0 0 1.0055803
19939 1.0055803 2.0861460 0 0 1 1.0055803
19940 0.0930588 2.0930588 0 1 1 0.0930588
19941 0.1013761 1.0221607 0 0 0 1.0221607
19941 1.0221607 2.1013761 0 0 1 1.0221607
19942 0.1030889 1.0005868 0 0 0 1.0005868
19942 1.0005868 2.1030889 0 0 1 1.0005868
19943 0.2029700 2.2029700 0 1 1 0.2029700
19944 0.0054617 1.0739532 0 0 0 1.0739532
19944 1.0739532 2.0054617 0 0 1 1.0739532
19945 0.2210836 2.2210836 0 1 1 0.2210836
19946 0.2123103 2.2123103 0 1 1 0.2123103
19947 0.0343030 1.0732966 0 0 0 1.0732966
19947 1.0732966 2.0343030 0 0 1 1.0732966
19948 0.0472326 1.0698422 0 0 0 1.0698422
19948 1.0698422 2.0472326 0 0 1 1.0698422
19949 0.1269767 2.1269767 0 1 1 0.1269767
19950 0.2143325 2.2143325 0 1 1 0.2143325
19951 0.0356413 2.0356413 0 1 1 0.0356413
19952 0.1026793 2.1026793 0 1 1 0.1026793
19953 0.1448503 2.1448503 0 1 1 0.1448503
19954 0.1413810 1.0062414 0 0 0 1.0062414
19954 1.0062414 2.1413810 0 0 1 1.0062414
19955 0.0620304 2.0620304 0 1 1 0.0620304
19956 0.1822886 2.1822886 0 1 1 0.1822886
19957 0.0340275 2.0340275 0 1 1 0.0340275
19958 0.1535778 2.1535778 0 1 1 0.1535778
19959 0.2079066 2.2079066 0 1 1 0.2079066
19960 0.1404790 2.1404790 0 1 1 0.1404790
19961 0.0970855 2.0970855 0 1 1 0.0970855
19962 0.2254987 1.0238882 0 0 0 1.0238882
19962 1.0238882 2.2254987 0 0 1 1.0238882
19963 0.1271343 2.1271343 0 1 1 0.1271343
19964 0.0433887 1.0269599 0 0 0 1.0269599
19964 1.0269599 2.0433887 0 0 1 1.0269599
19965 0.2143732 1.0521718 0 0 0 1.0521718
19965 1.0521718 2.2143732 0 0 1 1.0521718
19966 0.1759912 1.0401035 0 0 0 1.0401035
19966 1.0401035 2.1759912 0 0 1 1.0401035
19967 0.1502110 1.0192167 0 0 0 1.0192167
19967 1.0192167 2.1502110 0 0 1 1.0192167
19968 0.2194853 2.2194853 0 1 1 0.2194853
19969 0.1511083 1.0266629 0 0 0 1.0266629
19969 1.0266629 2.1511083 0 0 1 1.0266629
19970 0.1688953 2.1688953 0 1 1 0.1688953
19971 0.0979837 2.0979837 0 1 1 0.0979837
19972 0.1189600 1.0648144 0 0 0 1.0648144
19972 1.0648144 2.1189600 0 0 1 1.0648144
19973 0.1153122 2.1153122 0 1 1 0.1153122
19974 0.1479931 2.1479931 0 1 1 0.1479931
19975 0.0773806 1.0616583 0 0 0 1.0616583
19975 1.0616583 2.0773806 0 0 1 1.0616583
19976 0.1660984 1.0591965 0 0 0 1.0591965
19976 1.0591965 2.1660984 0 0 1 1.0591965
19977 0.0767413 2.0767413 0 1 1 0.0767413
19978 0.0302814 1.0404387 0 0 0 1.0404387
19978 1.0404387 2.0302814 0 0 1 1.0404387
19979 0.0374336 1.0606606 0 0 0 1.0606606
19979 1.0606606 2.0374336 0 0 1 1.0606606
19980 0.0511681 2.0511681 0 1 1 0.0511681
19981 0.1949129 2.1949129 0 1 1 0.1949129
19982 0.1479091 1.0151506 0 0 0 1.0151506
19982 1.0151506 2.1479091 0 0 1 1.0151506
19983 0.1990926 1.0536466 0 0 0 1.0536466
19983 1.0536466 2.1990926 0 0 1 1.0536466
19984 0.0632221 2.0632221 0 1 1 0.0632221
19985 0.0568474 2.0568474 0 1 1 0.0568474
19986 0.0410218 1.0584632 0 0 0 1.0584632
19986 1.0584632 2.0410218 0 0 1 1.0584632
19987 0.0491194 2.0491194 0 1 1 0.0491194
19988 0.0440717 1.0757358 0 0 0 1.0757358
19988 1.0757358 2.0440717 0 0 1 1.0757358
19989 0.1577719 2.1577719 0 1 1 0.1577719
19990 0.1692408 2.1692408 0 1 1 0.1692408
19991 0.0364190 2.0364190 0 1 1 0.0364190
19992 0.1480537 1.0300278 0 0 0 1.0300278
19992 1.0300278 2.1480537 0 0 1 1.0300278
19993 0.1572554 2.1572554 0 1 1 0.1572554
19994 0.0053831 1.0626797 0 0 0 1.0626797
19994 1.0626797 2.0053831 0 0 1 1.0626797
19995 0.2270365 2.2270365 0 1 1 0.2270365
19996 0.0062819 1.0161154 0 0 0 1.0161154
19996 1.0161154 2.0062819 0 0 1 1.0161154
19997 0.2145550 2.2145550 0 1 1 0.2145550
19998 0.0924497 2.0924497 0 1 1 0.0924497
19999 0.1404280 2.1404280 0 1 1 0.1404280
20000 0.1848871 1.0703519 0 0 0 1.0703519
20000 1.0703519 2.1848871 0 0 1 1.0703519
20001 0.1408773 2.1408773 0 1 1 0.1408773
20002 0.1220099 1.0466112 0 0 0 1.0466112
20002 1.0466112 2.1220099 0 0 1 1.0466112
20003 0.2203929 1.0543815 0 0 0 1.0543815
20003 1.0543815 2.2203929 0 0 1 1.0543815
20004 0.2088037 2.2088037 0 1 1 0.2088037
20005 0.0112215 2.0112215 0 1 1 0.0112215
20006 0.1567263 1.0514436 0 0 0 1.0514436
20006 1.0514436 2.1567263 0 0 1 1.0514436
20007 0.0057359 1.0315649 0 0 0 1.0315649
20007 1.0315649 2.0057359 0 0 1 1.0315649
20008 0.1868562 1.0054714 0 0 0 1.0054714
20008 1.0054714 2.1868562 0 0 1 1.0054714
20009 0.2161111 2.2161111 0 1 1 0.2161111
20010 0.1817446 1.0050345 0 0 0 1.0050345
20010 1.0050345 2.1817446 0 0 1 1.0050345
20011 0.0602516 2.0602516 0 1 1 0.0602516
20012 0.1879564 2.1879564 0 1 1 0.1879564
20013 0.1231223 1.0347821 0 0 0 1.0347821
20013 1.0347821 2.1231223 0 0 1 1.0347821
20014 0.2213351 1.0582583 0 0 0 1.0582583
20014 1.0582583 2.2213351 0 0 1 1.0582583
20015 0.0024073 2.0024073 0 1 1 0.0024073
20016 0.1285458 1.0322765 0 0 0 1.0322765
20016 1.0322765 2.1285458 0 0 1 1.0322765
20017 0.1928789 2.1928789 0 1 1 0.1928789
20018 0.1013682 1.0728013 0 0 0 1.0728013
20018 1.0728013 2.1013682 0 0 1 1.0728013
20019 0.2059985 2.2059985 0 1 1 0.2059985
20020 0.1339923 1.0404585 0 0 0 1.0404585
20020 1.0404585 2.1339923 0 0 1 1.0404585
20021 0.0780615 2.0780615 0 1 1 0.0780615
20022 0.1231370 2.1231370 0 1 1 0.1231370
20023 0.0735200 1.0396495 0 0 0 1.0396495
20023 1.0396495 2.0735200 0 0 1 1.0396495
20024 0.1199728 2.1199728 0 1 1 0.1199728
20025 0.0560020 2.0560020 0 1 1 0.0560020
20026 0.0430323 1.0516635 0 0 0 1.0516635
20026 1.0516635 2.0430323 0 0 1 1.0516635
20027 0.1594245 1.0369435 0 0 0 1.0369435
20027 1.0369435 2.1594245 0 0 1 1.0369435
20028 0.0132445 2.0132445 0 1 1 0.0132445
20029 0.0005264 1.0595639 0 0 0 1.0595639
20029 1.0595639 2.0005264 0 0 1 1.0595639
20030 0.0505422 2.0505422 0 1 1 0.0505422
20031 0.1250886 1.0353125 0 0 0 1.0353125
20031 1.0353125 2.1250886 0 0 1 1.0353125
20032 0.0741808 1.0007734 0 0 0 1.0007734
20032 1.0007734 2.0741808 0 0 1 1.0007734
20033 0.1416346 2.1416346 0 1 1 0.1416346
20034 0.1921256 1.0524930 0 0 0 1.0524930
20034 1.0524930 2.1921256 0 0 1 1.0524930
20035 0.0789389 1.0363147 0 0 0 1.0363147
20035 1.0363147 2.0789389 0 0 1 1.0363147
20036 0.0787620 1.0668821 0 0 0 1.0668821
20036 1.0668821 2.0787620 0 0 1 1.0668821
20037 0.2165541 2.2165541 0 1 1 0.2165541
20038 0.1319916 2.1319916 0 1 1 0.1319916
20039 0.1743019 2.1743019 0 1 1 0.1743019
20040 0.0352606 1.0425210 0 0 0 1.0425210
20040 1.0425210 2.0352606 0 0 1 1.0425210
20041 0.1315487 1.0591534 0 0 0 1.0591534
20041 1.0591534 2.1315487 0 0 1 1.0591534
20042 0.1735809 2.1735809 0 1 1 0.1735809
20043 0.1100964 1.0307287 0 0 0 1.0307287
20043 1.0307287 2.1100964 0 0 1 1.0307287
20044 0.1136543 1.0313795 0 0 0 1.0313795
20044 1.0313795 2.1136543 0 0 1 1.0313795
20045 0.0870165 1.0721246 0 0 0 1.0721246
20045 1.0721246 2.0870165 0 0 1 1.0721246
20046 0.1699211 2.1699211 0 1 1 0.1699211
20047 0.0392643 2.0392643 0 1 1 0.0392643
20048 0.0679735 2.0679735 0 1 1 0.0679735
20049 0.1740315 1.0127555 0 0 0 1.0127555
20049 1.0127555 2.1740315 0 0 1 1.0127555
20050 0.0578692 2.0578692 0 1 1 0.0578692
20051 0.1597695 1.0225240 0 0 0 1.0225240
20051 1.0225240 2.1597695 0 0 1 1.0225240
20052 0.0528353 2.0528353 0 1 1 0.0528353
20053 0.0158613 1.0060343 0 0 0 1.0060343
20053 1.0060343 2.0158613 0 0 1 1.0060343
20054 0.1317004 1.0435291 0 0 0 1.0435291
20054 1.0435291 2.1317004 0 0 1 1.0435291
20055 0.0677244 2.0677244 0 1 1 0.0677244
20056 0.0916920 1.0029379 0 0 0 1.0029379
20056 1.0029379 2.0916920 0 0 1 1.0029379
20057 0.1320341 1.0046341 0 0 0 1.0046341
20057 1.0046341 2.1320341 0 0 1 1.0046341
20058 0.0381565 2.0381565 0 1 1 0.0381565
20059 0.0419602 1.0752237 0 0 0 1.0752237
20059 1.0752237 2.0419602 0 0 1 1.0752237
20060 0.0500690 2.0500690 0 1 1 0.0500690
20061 0.0160610 2.0160610 0 1 1 0.0160610
20062 0.0722639 1.0218254 0 0 0 1.0218254
20062 1.0218254 2.0722639 0 0 1 1.0218254
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29990 0.1326219 2.1326219 0 1 1 0.1326219
29991 0.2074962 2.2074962 0 1 1 0.2074962
29992 0.1237438 1.0349485 0 0 0 1.0349485
29992 1.0349485 2.1237438 0 0 1 1.0349485
29993 0.0169895 2.0169895 0 1 1 0.0169895
29994 0.1016634 1.0092151 0 0 0 1.0092151
29994 1.0092151 2.1016634 0 0 1 1.0092151
29995 0.1202777 2.1202777 0 1 1 0.1202777
29996 0.1324033 2.1324033 0 1 1 0.1324033
29997 0.1146650 2.1146650 0 1 1 0.1146650
29998 0.0352067 1.0214708 0 0 0 1.0214708
29998 1.0214708 2.0352067 0 0 1 1.0214708
29999 0.0731609 2.0731609 0 1 1 0.0731609
30000 0.1452800 2.1452800 0 1 1 0.1452800

Inference

We’ll fit two models. The first is the true data generating model, where VE decays linearly on the log hazard scale. Second, we’ll model the VE decay profile using a P-spline. In practice, it is important in both of these models to recognize that we need to evaluate the value of the time-varying VE profile for each participant at each event time, not just at the failure time of that particular participant. The tt() functionality in the survival package will facilitate this.

We’ll start with the log-linear decay model

# Cox PH model with log-linear decay
# note that time since vaccination is a time-varying parameter.
# also, vacc is a time-varying covariate.
fit_lin = 
  coxph(formula =
                  Surv(time = tstart, 
                       time2 = tstop, 
                       event = status) ~ vacc + tt(tvacc), 
              tt = function(tvacc, t, ...) {
                  pmax(0, t - tvacc)
              },
              data = simr_waning)

fit_lin
## Call:
## coxph(formula = Surv(time = tstart, time2 = tstop, event = status) ~ 
##     vacc + tt(tvacc), data = simr_waning, tt = function(tvacc, 
##     t, ...) {
##     pmax(0, t - tvacc)
## })
## 
##              coef exp(coef) se(coef)      z        p
## vacc      -2.1890    0.1120   0.2220 -9.862  < 2e-16
## tt(tvacc)  1.3291    3.7777   0.2577  5.158 2.49e-07
## 
## Likelihood ratio test=132.5  on 2 df, p=< 2.2e-16
## n= 44890, number of events= 292

And now we fit the P-spline decay model.

# p-spline decay model. again, time since vaccination is a time-varying
# parameter and vacc is a time-varying covariate.
fit_ps = 
  coxph(formula =
                  Surv(time = tstart, 
                       time2 = tstop, 
                       event = status) ~ vacc + tt(tvacc),
              tt = function(tvacc, t, ...) {
                  pspline(pmax(0, t - tvacc), df = 3, nterm = 8)
              },
              data = simr_waning)

fit_ps
## Call:
## coxph(formula = Surv(time = tstart, time2 = tstop, event = status) ~ 
##     vacc + tt(tvacc), data = simr_waning, tt = function(tvacc, 
##     t, ...) {
##     pspline(pmax(0, t - tvacc), df = 3, nterm = 8)
## })
## 
##                     coef se(coef)    se2  Chisq   DF       p
## vacc              -2.256    0.456  0.386 24.452 1.00 7.6e-07
## tt(tvacc), linear  1.285    0.262  0.262 23.948 1.00 9.9e-07
## tt(tvacc), nonlin                         5.312 2.05   0.074
## 
## Iterations: 4 outer, 11 Newton-Raphson
##      Theta= 0.809 
## Degrees of freedom for terms= 0.7 3.1 
## Likelihood ratio test=139  on 3.77 df, p=<2e-16
## n= 44890, number of events= 292

The survival package nicely partitions the P-spline into a linear and non-linear trend. The non-linearity is not statistically significant. We also can test for time-varying VE in each model using a likelihood ratio test. We refit the models without the decay terms, and then calculate our LRT test statistics which are compared to chi-square distributions with degrees of freedom equal to the change in the number of parameters (or effective number of parameters, in the case of the P-spline) between the unrestricted and restricted models. Both tests emphatically reject the null hypothesis of constant VE.

# model without waning VE
lin_nowaning = update(fit_lin, .~. - tt(tvacc))
ps_nowaning = update(fit_ps, .~. - tt(tvacc))
    
# likelihood ratio test for waning VE
lin_lrt_pval = 
    1 - pchisq(2 * (fit_lin$loglik - lin_nowaning$loglik)[2], df = 1)
    
ps_lrt_pval = 
  1 - pchisq(2 * (fit_lin$loglik - lin_nowaning$loglik)[2], df = fit_ps$df[2] - 1)

# print p-values
lin_lrt_pval
## [1] 2.718607e-08
ps_lrt_pval
## [1] 2.138699e-07

We next extract the model estimates and covariance matrices and plot VE(t). The parameterization of P-splines in the survival package is a bit odd so we have to recenter the spline term.

# estimates of VE(t)
VE_ests = 
  expand.grid(time = seq(0,2,by=0.01),
              Model = c("log-linear", "P-spline"))

VE_ests$truth = log(0.15) + 0.977558 * VE_ests$time

times_lin = cbind(1, seq(0,2,by=0.01))
times_ps = cbind(1, pspline(seq(0,2,by=0.01), df = 3, nterm = 8))
centvec = rep(0, ncol(times_ps)); centvec[2] = 1 # for centering the spline
centvec = rep(1, ncol(times_ps)) %*% diag(centvec)

VE_ests$est = 
  c(times_lin %*% coef(fit_lin),
    apply(times_ps, 1, function(x) (x - centvec) %*% coef(fit_ps)))

VE_ests$lower = 
  VE_ests$est - 1.96 * c(
    sqrt(apply(times_lin, 1, function(x) t(x) %*% vcov(fit_lin) %*% x)),
    sqrt(apply(times_ps, 1, function(x) (x - centvec) %*% vcov(fit_ps) %*% t(x - centvec))))

VE_ests$upper = 
  VE_ests$est + 1.96 * c(
    sqrt(apply(times_lin, 1, function(x) t(x) %*% vcov(fit_lin) %*% x)),
    sqrt(apply(times_ps, 1, function(x) (x - centvec) %*% vcov(fit_ps) %*% t(x - centvec))))
require(ggthemes)
VE_ests %>% 
  ggplot(aes(x = time)) + 
  geom_line(aes(y = truth, linetype = "Truth"), linetype = "dashed") + 
  geom_ribbon(aes(ymin = lower, ymax = upper, fill = Model), alpha = 0.4) + 
  geom_line(aes(y = est, colour = Model)) + 
  facet_grid(. ~ Model, scales = "free") + 
  theme_minimal() +
  scale_color_tableau(palette = "Tableau 10", direction = -1) +
  scale_fill_tableau(palette = "Tableau 10", direction = -1) +
  scale_y_continuous(breaks = seq(-3, 2.5, by = 1),
                     labels = round(1 - exp(seq(-3,2.5,by=1)), digits = 1)) +
  labs(x = "Years since vaccination", y = "Vaccine efficacy", 
       title = "Vaccine efficacy vs. years since vaccination") + 
  theme(legend.position = "none",
        text = element_text(family = "serif", size = 20))

References